How to use skills — did this change between editions and how?

Question

It seems the role of rules¹ was changed throughout the history of D&D. For instance, as this answer says, there was an explicit destinction between "crunch" and "fluff" in fourth edition:

a distinction between "ignorable fluff" and the "real rules"

Such a separation is a prominent feature of 4e

Were there any changes on how the rules were supposed to be interpreted regarding characters' Skills?

I'm primarily interested in the most popular "modern-ish" editions, so narrowing the question, what changes considering Skills were introduced in 5e in comparison to 3.5e? Were there any changes about how Skills are supposed to be used, when players make checks, what results do they get, etc.?

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¹: By "the role of rules" I mean "how the rules are meant to be used in order to run a game".

Answer 1

There's indeed a difference between 3.x and 5 paradigm

After a little research I came to conclusion that the role of rules in 3.5e and 5e does differ:

• 3.5e rules serve like a rigid framework, that explicitly says, what mechanics we must use and when

• 5e rules are more like a toolset, where choosing the right tool is a subject of the DM's discretion

How Skill checks are supposed to be made in 3.x

3.5 edition goes from the concept of "character uses a skill":

When your character uses a skill, you make a skill check to see how well he or she does.

Pathfinder define this even stricter, explicitly describing when "you must make a skill check":

When your character uses a skill, he isn’t guaranteed success. In order to determine success, whenever you attempt to use a skill, you must make a skill check.

So, you say "I use my Search skill", for example. Then you have to roll what the game rules want you to roll. Then you get a particular result from the list pre-written in the rules. Then you use this skill again (and roll once more) because the circumstances changed. This could lead to a lot of unneeded dice rolls.

This is not how skills work in 5th edition

The latest edition removed "skill checks" completely. It was not just about renaming "skill check" to "abilty check with a proficiency bonus", it's actually a new approach (an old one, actually — that's how the rules were used in 2.x edition) — the DM asks for a dice roll when they think it is necessary:

When the outcome is uncertain, the dice determine the results.

See these questions for more details:

• Can players declare that they are making a specific ability check?
• When climbing certain terrains that require an Athletics check, do you need to make the check again every turn?

The "How to play" chapter describes the game process in three steps and does not even mention any mechanics. Instead, players are supposed to describe, what their character do in the game world. DMG says the game can be played without dice at all (the only exception is combat), if the DM thinks there was no uncertainty to determine, as being said in "The Role of Dice":

The DM calls for an ability check when a character or monster attempts an action (other than an attack) that has a chance of failure. When the outcome is uncertain, the dice determine the results.

The rules use words "might" or "can" in most cases regarding checks which are made out of combat:

the DM might call for a Wisdom (Animal Handling) check

5th edition empowers the DM in ways that 3rd, 3.5, and 4th did not. While rule zero has always applied, 5th edition chooses not to explicitly codify many things. DMG address this in the beginning of the first chapter:

The rules serves you, not vice versa

Jeremy Crawford, the lead game designers, supports this idea in several interviews, (for instance, this Dragon Talk around 45:15).

"...we tried to make every piece of the game to feel like a tool that players and DMs can pick up and use with consistency"

Answer 2

Interpretation of ambiguous or undefined rules

• In 3.5, the Dungeon Master's Guide, p.6, "Adjudicating", advises DMs to interpret unclear situations by extrapolating from other similar rules.
• In 5e, the traditional interpretation is that rules say what they say and no more. Anything else is up to the DM. There are no official guidelines for situations not covered by the rules, other than that the DM decides, and the DM sometimes rolls dice (PHB p.6).

Precedence of rule sources

• In the 3.5 Dungeon Master's Guide, p.6, "Adjudicating", rulebooks take precedence over adventure modules (except for adventure-specific situations). By the D&D 3.5 errata, each core rulebook is considered the primary rulebook over its particular field. By the Rules Compendium, p.5, "Order of Rules Application", specific beats general, and an exception breaks either specific or general.
• In 5e, specific beats general (PHB p.7). No one rulebook has precedence over another.

Clarity of FAQ entries

• The 3.0 and 3.5 FAQ were notorious for inventing rulings without making it clear that these were the Sage's own rulings rather than a direct interpretation of the rules.
• The 5e FAQ makes clear distinctions between Rules As Written (RAW; the rules say what they say and no more), Rules As Intended (RAI; what the designers meant) and Rules As Fun (RAF; what would be reasonable and cool).
  _{(The "FAQ" are referred to as the Sage Advice Compendium in this edition}