What exactly is the difference between Attack action and attack?
It seems each time a question regarding this pops up, there's always somebody arguing they are not different. I feel there should be a concise and indisputable answer that shows how they are, in fact, different.
The "Actions in Combat" section of the Player's Handbook (PHB, page 192) states (emphasis mine):
When you take your action on your turn, you can take one of the actions presented here, an action you gained from your class or a special feature, or an action that you improvise [...]
The use of "or" clearly means that class features and the "action listed here" are distinct actions. The first action listed is "Attack"; the "Attack action" (emphasis mine):
The most common action to take in combat is the Attack action [...] With this action, you make one melee or ranged attack.
This, and the above quote, clearly show that the Attack action and attacks are different things. There is only one Attack action, which is why it is defined alongside the other actions such as Dodge, and Hide.
Regular attacks are defined in the "Making an Attack" section (PHB, page 194):
If there’s ever any question whether something you’re doing counts as an attack, the rule is simple: if you’re making an attack roll, you’re making an attack.
Bringing all this together: the Attack action is a specific action that anybody can take whereas class granted features and abilities, such as the Ranger's Volley, are not Attack actions, but instead their own individual actions even though they may happen to involve attack rolls.
In conclusion: There is the "Attack action", which is a specific action and there are "attacks", which are anything involving an attack roll. The easiest way to tell these apart is that one is followed by the word "action" and the other is not.
As Nitsua60 correctly points out in his answer:
A close reading of the PHB makes clear this is a place where the authors have been very consistent and explicit in differentiating: you'll always see phrases like "make an attack" and "take the Attack action," never "make an Attack" or "take the attack action." See PHB pp. 49, 63, 72, 74, 78, 79, 85, 92, 93, 111, 165, 168, 170, 192, 195, for some examples of their consistent and exacting capitalization." (see their answer below for more details)
Icyfire also correctly points out in their answer that capitalization isn't perfect; the best way to distinguish between these terms is simply by whether or not the word "attack" is followed by the word "action" (see their answer for more details).
Another reason capitalization isn't perfect is that many sites, including Roll20, completely butcher the capitalization of the actual rulebooks by capitalizing countless words that were not capitalized originally. This means capitalization is not something you should rely on for clarity, and instead you should go by whether it says "an attack" or "the attack action".
Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn....
This helps to showcase the difference between the two. If "attack" and "Attack action" were synonymous and thus making an attack meant taking the Attack action, then the Feature could simply read "You can attack twice, instead of once, on your turn."
This type of reading would also lead to allowing for infinite attacks in a turn - clearly not the intended reading.
Note: This feature is not an action nor attack of its own, but a passive feature which activates "whenever you take the Attack action on your turn".
Also Note: The reason "Extra Attack" is capitalized is the same reason any feature would be capitalized: because it is a specific/proper phrase/noun.
When you take the Attack action and attack with a light melee weapon...
Again if "Attack action" and "attack" were synonymous then this sentence is redundant and could be reduced to "When you attack with a light melee weapon", the fact that it is not reduced further shows that they are two different things.
In order to cast most spells you must use your action to take the "Cast A Spell" action. If "attack" and "Attack action" were the same thing and you were casting, say, fire bolt, a spell which has an attack roll, then you would have to use the "Cast A Spell" action but then you would have to take the "Attack" action as well (as you are making an attack). This is clearly impossible as you, generally, only have one action per turn.
Thus we can conclude that something having an attack roll does not make it require the "Attack action" or else a consequence would be the inability to cast spells with attack rolls.
[...] you can use the Attack action to make a special melee attack, a grapple. [...]
Using the Attack action, you can make a special melee attack to shove a creature [...]
These are attacks made using the Attack action and are specifically called out in the rules as being "special". They are special for two reasons. First, they do not involve attack rolls, but are still considered attacks. And second, because they replace attacks made as part of the Attack action, and not just any attack. The best example of this is opportunity attacks, which cannot be a grapple or a shove as you are not taking the Attack action but instead a reaction that involves an attack.
Both of the answers from nitsua60 and Medix2 are correct regarding the nature of the distinction. However, the distinction is between the phrases "Attack action" and the word "attack," not between capitalizations.
For completeness, an Attack action is a type of action that can be taken, defined on PHB 192:
The most common action to take in combat is the Attack action, whether you are swinging a sword, firing an arrow from a bow, or brawling with your fists... Certain features, such as the Extra Attack feature of the fighter, allow you to make more than one attack with this action.
Whereas an attack is defined as anything that requires an attack roll (PHB 194):
If there’s ever any question whether something you’re doing counts as an attack, the rule is simple: if you’re making an attack roll, you’re making an attack.
An Attack action can contain an attack, but it can also contain multiple attacks as well as grapples and shoves, among other things. In accordance with its name, using an Attack action uses up your action for the turn. On the other hand, an attack is usually contained within some other attempted thing: a spell, a melee weapon strike, etc.
Whenever the text is referring to an action, it is explicitly called an Attack action. Capitalization is not always a reliable way to determine whether or not the text is referring to the action--instead, one has to focus on the context. Attack actions are always written as such, whereas the other kind of attack frequently carries a modifier with it, such as "melee weapon attack" or "spell attack" or such. I have not found an exception to this rule in the PHB.
This is most commonly clear in the MM, where monsters' melee weapon attacks are all capitalized as "Melee Weapon Attack". Clearly these attacks are not attack actions, but they are capitalized as part of the header. If we focused only on the capitalization, we would have to look to context to determine whether it's an Attack action or just an attack.
I realize that this difference might be splitting hairs, but it's useful for resources that are not as careful as the PHB. For example, the official rules in the roll20 compendium or other SRD websites are not always so careful to preserve the capitalizations, but they usually do a good job in preserving the proper wording. Focusing on capitalization rather than terms of art might lead to frequent confusion.
An attack is a bit of action that a character can take: it involves choosing a target, determining modifiers, and resolving the outcome (PHB p.192).* This may happen:
An Attack is shorthand for "choosing the defined Attack action from among the defined actions I might choose" and includes at least one attack.
* - except in the cases of Shove and Grapple, which are explicitly called out as exceptions to that "attack roll" <--> "attack" equivalence.
A close reading of the PHB makes clear this is a place where the authors have been very consistent and explicit in differentiating: you'll always see phrases like "make an attack" and "take the Attack action," never "make an Attack" or "take the attack action." See PHB pp. 49, 63, 72, 74, 78, 79, 85, 92, 93, 111, 165, 168, 170, 192, 195, for some examples of their consistent and exacting capitalization.
But you could be forgiven for thinking "am I really going to hang something on believing they proofread that well? (After all, look at the instances of "can make a save" vs. "make a save" vs. "must make a save." It's not at all clear that those would survive the standard I'm setting in point 1.) Luckily, here comes point 2:
Consider what it would mean if they weren't different. For instance, look at the (roughly) 27 PHB+EEPC spells that require an attack roll. If attack=Attack, then casting a spell with an attack roll means you're Attacking. Which requires taking the Attack action. But you also need to take the Cast a Spell action. Do we believe that the reading "attack spells can only be cast by hasted or Action Surging casters" is really the intent?
The reading that "attack" = "Attack" nigh-moots every caster's attack cantrips. There may be arguments for choosing to play a game like that, but it's not the game WotC wrote, best I understand.
