None of your scenarios are quite correct. The answer to this is found in Chapter 9: Combat of the Player’s Handbook or the Basic Rules, under “Actions In Combat”:
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.
With this action, you make one melee or ranged attack. See the "Making an Attack" section for the rules that govern attacks.
Certain features, such as the Extra Attack feature of the fighter, allow you to make more than one attack with this action.
The key here is that “taking the Attack action” is different to “making an attack”.
- Making an attack, as per Chapter 9, means choosing a target, making an attack roll, and if you hit, making a damage roll and dealing damage. (You can also forgo trying to do damage, and use your attack to attempt to grapple or shove your target, which works a little differently.)
- Taking the Attack action is an action available to all characters that allows them to make an attack in combat. There are other ways to make an attack - opportunity attacks, specific class features, casting certain spells (e.g. booming blade) etc - but this is the basic, universal one.
Extra Attack modifies the Attack action for Fighters (and other classes that receive the feature) so that they make two attacks - i.e. they “make an attack” twice (or more at later levels).
So the correct description in your style is:
- You make an attack (choose a target; roll a d20 to see if you hit; roll damage if you hit); then if you wish, make another attack (choose a target; roll a d20 to see if you hit; roll damage if you hit).
I’ll also add that taking the Attack action doesn’t automatically end your turn, regardless of how many attacks you get to make. As is the case with most actions, you can also:
- take one bonus action if you haven’t already, and have a valid one available (two-weapon fighting and some class features, like Flurry of Blows, even require you to take the Attack action before you can use them);
- do something that doesn’t count as an action (speak briefly, interact with one object, use certain class features etc); and
- move, if you have movement left (you can even move in between your multiple attacks).