Third edition introduced skills into D&D. Before that there were the Thief skills, which were really just special abilities with a percentile chance of success and by 2nd edition AD&D and the Rules Cyclopedia there were also Non-weapon Proficiencies. NWPs used the system that described a character's proficiency with weapons to showcase the character's abilities and skills in different areas. There was a list but the game suggested to create your own. In many ways these were like Traits or even Aspects from other games. If your experience in the field applied, you got a bonus to your roll.
Now, Proficiencies before 3E were a lot like feats later on. And since 3E has mutated into 4E and Pathfinder, the idea of "Proficient vs Non-Proficient" has crept back in through the back door. In 4E you automatically get half your level to your skill rolls, and if you're proficient in the skill you get an extra bonus on top of that. In Pathfinder, if you invest a single point into a class skill, you get an extra +3 bonus to it.
3rd Edition also introduced feats. In 3.x, there's a feat called Endurance. It gives you a +4 bonus to: "Swim checks made to resist nonlethal damage from exhaustion; Constitution checks made to continue running; Constitution checks made to avoid nonlethal damage from a forced march; Constitution checks made to hold your breath; Constitution checks made to avoid nonlethal damage from starvation or thirst; Fortitude saves made to avoid nonlethal damage from hot or cold environments; and Fortitude saves made to resist damage from suffocation."
That's a whole lot of bonuses all over the place. 4E and certain collections of houserules throw this feat out in favor of a skill called Endurance that covers all the above-mentioned rolls. We see how feats and skills intersect in various places.
But if a skill is really d20 + ability + proficiency [+level-dependent bonus] the question becomes what is the difference between a skill check and an ability check. A skill check is just an ability check where your proficiency bonus applies (and we're back at the start). The only difference is the level-dependent benefit (the half-level bonus in 4E or the ranks invested after first level in 3.X) - but that's just an artefact of level bloat. It has bugged me from day 1 that the DCs for Ability checks shouldn't really scale with level, but the DCs for skill checks should. Why? A difficult door to kick down (Str check) is always going to be the same DC but to unlock a difficult lock you'll technically have to roll higher and higher numbers.
I've looked at Saves from a similar angle in my old "why are there no Saves in Subterranean Adventures" post. Everything should revert back to being an ability check.
This is of course my personal preference, which not everyone will share. There are several reasons why I like it. For one, it resolves a lot of moments where it's not exactly clear what the players should roll.
We've all been there when a character slips off a ledge or off the edge of a cliff and another player yells "I catch him!". What is the appropriate roll for that? A reflex save? A dexterity check? A touch attack? An athletics roll? An initiative roll?
Having fewer, but more clearly-defined rolls, makes it far far easier to figure out what should be rolled. And the bonuses from proficiency, feats, abilities, powers, items etc. apply as they apply. Which brings me to part two.
On the skill list in 3.X there's also the Profession skill. It's actually Profession (_______) and you're supposed to fill in the blank. Now, this already looks suspiciously like the NWPs from 2nd edition, but let's carry on. In an effort to codify everything, the mechanical effect of the Profession skill was described as earning money, taking one week to complete.
Not only does this make the skill virtually useless in most actual play (it might be useful in a game where everyone is a farmer or otherwise employed person, but then what are all these spells and special abilities for - it's just one skill!), it also doesn't make much sense. Firstly, the amount of adventuring a character can do in a week will always net them tens or even hundreds more gold than one week of work. Secondly, let's say a character has the Profession (Sailor) skill.
The character is on a ship in a storm and has to climb some ropes. Now what do we roll for that? By the book, it's a Climb check. Even if the character is an excellent Sailor, with ten or more ranks in the skill, she can't climb the ship's ropes for crap if she didn't also take the Climb skill. Which means the player has to spend double the resources to actually make the character good at what she's supposed to be good at. On the other hand, if the DM allows the player to make a Profession (Sailor) check instead, then suddenly the skill becomes unwieldy and possibly overpowered, as it can do far more things than an ordinary skill, the job of several skills at once, for less investment. That makes no sense and is usually avoided.
Profession thus becomes one of the most useless skills in the game. There is absolutely no reason to take it, ever, except perhaps for some vague notion of "roleplaying" and mechanically describing your character concept. Except it's actually harmful to your character concept and not conductory to roleplaying whatsoever, since taking the Profession (Sailor) skill actually makes your character a worse sailor than she would be if you had invested those same points into Acrobatics, Climb, Use Rope (or whatever) skills instead. Except she also inexplicably somehow earns more money than all the sailors that are actually good at their job.
(I'm ignoring the whole deal about how D&D is about adventuring 99% of the time and investing points into stuff like Profession (shepherd) harms your character from an effectiveness point anyway, since you're going to be worse at actually important adventuring stuff like Perception or Stealth.)
Observation A: skills can always be transformed into feats (like the Tumble skill from 3.x could have been a feat that allowed you to move without provoking AoOs), feats into skills (like the Endurance example I mentioned above) and skills can always be treated as ability checks with a special bonus or two.
Observation B: Before skills, general skills were Proficiencies, and Proficiencies were feats.
Let's call them all by a single name. Like Proficiencies. Or Traits. Or whatever. Let's just say Features.
Observation C: There are lines between Adventuring features, Character concept features and Class features.
Class: There are certain feats and skills a class will always take, thus making them redundant (like Concentration for Wizards in 3.x or Power Attack for basically all melee characters). These are class defaults.
Character skills and feats like Profession (basketweaver) should not draw from the same budget than Adventuring features.
Thus, my ideal: all Barbarians have Power Attack (eventually) [much like all wizards simply have Concentration - and Pathfinder acknowledged this (and the way the Concentration skill was turned into a caster level check in Pathfinder is very reminiscent of how all skills were changed in 4E)]. Not all Barbarians have Perception, but whether or not they do does not depend on whether or not they also have Profession (basketweaver). Three different resource pools. Class level, Skill and Background.
So any way you look at it, you should always roll d20+relevant ability then bonuses from any features, if they apply. Only then does +level or +1/2 level or +ranks (per level) or whatever feature into it. And the question is, is that last bit really necessary? From an objective standpoint, it just screws up the math in the long run. But it's part of the legacy, much like ever-increasing HP.
I started writing this post with a completely different objective in mind, but I guess I had to say all this anyway.