Except I was around when the thief came into existance, and other that whatever they called secret strike back then, it was nothing but skills. Seriously. There was nothing else distinct about it, and it was, when if first arrived, unique in that way.
Basically, I don't see your characterization of them as anything but a high end expression of skills in that area. And that was absolutely the way they worked initially, to the degree they worked at all.
I was too. "Backstab" was the original term, I believe.
And it was absolutely an expression of skills. Importantly, it was the only class that had skills rather than powers. (Hide in Shadows vs. Turn Undead) No one else had skills. If anyone else wanted to do things it was a 1 in 6 chance*, better if there were extenuating circumstances. These skills were also watered down in successive editions. Climb Sheer Surfaces became Climb Walls. Anyone could climb walls; the character had to remove all metal armor, be unencumbered, and had a bonus to their d6 roll if they had a rope. Thieves could freeclimb even with their backpack and gear. The other skills were similarly advantaged in theme.
And, as you note, as the class system transitioned to adding an initial engine-wide skill system, powers were added to the classes to strengthen their niche and archetype. So, in D&D there is more than a simple skill package to typify a "thief". The powers available might be unique to PC thieves, and NPCs only have the skill package.
I think which is why I disagree with the concept of "skill-monkey", especially in a class-based system. The Thief isn't a jack-of-trades character. They are the class that is supposed to be the best at stealth in an urban environment. I extend that to being the class most adept at urban environments: moving through, finding people, establishing networks, knowing who owes whom, &c. What I found to be an excellent JoT character is the Akashic from
The Diamond Throne that Monte Cook initially published (now owned by someone else). They are the "skill-monkey" people want.
So, to sum up, if you are looking just at skills to describe a character, then, yes, there isn't much to differentiate different skill packages such as warrior captain, cat burglar, herbalist, woodsman, &c. If you are looking at a class system, then, no, there is more to describe a particular class than the skills, it's the attendant class abilities. And, if the class in question is the only one with skills, the differentiation isn't the "skill package". The skills
are the powers.
* This is why thief skills started at 15-20% in AD&D. Succeeding 1 in 6 is a 16.7% chance. Thieves started as good as anyone else, but since a percentile system was used they could more easily and with finer granularly increase in ability with increasing level. Although that was only with humans. A group of elvish wizards or halfling fighters in leather could surprise a monster 4 in 6. A human thief had to be 9th level to reach that peak!
PS: I have played in a skill-less D&D where there was only seven classes tied to the attributes. Fighter, Magic-user, Cleric,
Skirmisher, Monk, Bard, (Elf-taught FTR/MU with a unique name I forget). All "skill checks" were tied to the prime requisite, roll 3-5d6 to match or lower. Anyone could try to sneak, but the skirmisher rolled 3 dice to the other classes 4. A wizard trying to sneak rolled 5 dice.
NB: One of the original expressions of the thief submitted to the Strategic Review had thief abilities expressed in times per day, following a similar mechanic as magic-users. Gary went with a skill cluster for whatever reason, probably Dave-influenced.. 
