"I want to play a merchant," "I want to play an archer," "I want to play a vagabond." What classes are represented in those statements? Can you tell? The proper answer is: no, you can't, because classes aren't occupations or descriptions, they're just bundles of abilities that belong to certain types of people. They're archetypes, not jobs. Imagine a system that had to build a separate class for every job in the universe -- what would a baker class be like? Why would every baker follow the same general progression? You can see where this is going: eventually the classes would become infinitely granular to the point where EVERY INDIVIDUAL would need their own class (or at least every conceivable job in every conceivable culture viewed through every conceivable lens).
Character classes in AD&D are not jobs. They do not describe what you do, but rather what you have in common with certain other people. Indeed, AD&D takes the somewhat war-gamey point of view that essentially all people are, at a certain level, interchangeable. The skills of one fighter are not really all that different than the skills of another. Perhaps one favors a different weapon, or the other is just plain stronger. Perhaps one is more skilled, which is an important distinction to make in a roleplaying game.
What doesn't AD&D model? It doesn't model knowing "techniques" very well. It assumes a common canon of combat knowledge between characters. Getting better happens in general, not specific. You don't increase your ability to, say, trip someone without also increasing your ability to fight in general.
Back to the first question: what would the classes be to represent those first three characters I mentioned? Well, you could go a number of ways. A merchant could easily be a low level fighter or a thief. An archer goes either way there too. A vagabond could be a fighter, a thief, a bard, or even a wizard. Why? Because these are ciphertitles. Classes don't describe what you do, they describe how you do it.
I don't understand the hypergranular and yet completely non-intuitive class system of 3.x. I don't like the straightjacket classes of 4e. Classless systems are actually pretty alright by me as well. But if you're going to come and play AD&D, don't complain that all fighters are the same. They're not, they just have similar skill sets. It's what happens when a man learns to fight instead of, say, steal.