Honestly, I kinda think that trying to explain specific moves is asking for trouble. There’s such a massive variety of attacks, almost all of which are available to many different Pokémon, that you’re bound to get stuff that’s absolutely ludicrous when you stop to think about it. Surf conjuring a wave out of nothing is a bit strange, but really it’s an extension of the way Water moves in general conjure water out of nothing (there’s no way a Squirtle can have enough water inside his own body to sustain a Water Gun for more than a few seconds). And I don’t think anyone knows how Baton Pass is supposed to work.
In general, I like moves that are relatively exclusive, because those are the ones that have a very specific meaning in terms of the nature of a Pokémon’s powers. Signature moves, obviously, but also stuff like Moonlight, as you mentioned, or Morning Sun, which have some nice flavour connotations for the sources of energy a Pokémon uses (Morning Sun, for instance, is a far more exclusive technique than Synthesis and is connected with Pokémon like Espeon, Togetic and Volcarona, suggesting that Pokémon who use it are drawing on sunlight for energy in a far more abstract, ‘magical’ sense than Pokémon who use Synthesis). Aura Sphere is another, which implies a connection with some sort of ‘soul energy’ or whatever you want to call it.
Conversely, it’s the moves that are the most widely available that tend to bug me, because those are the ones that are most likely to belong to Pokémon who have no business using them. Everyone brings up Focus Punch, which is available to a couple of clearly armless Pokémon like Togekiss, but my personal favourite is Aerial Ace. Now, yes, I know Aerial Ace is supposed to be a reference to an old Japanese sword move, the ‘turning swallow cut,’ but 1. it’s a Flying-type attack, 2. the only Pokémon who learn it by levelling are bird Pokémon (and… er… Heracross… for some reason… although Heracross can actually fly), and 3. whether you imagine it requiring flight or not, it carries connotations of extreme speed. Aerial Ace is available to a number of Pokemon who blatantly cannot fly and, in some cases, weigh hundreds of kilograms, including Tyranitar, Ursaring, Tangrowth, Metagross, Nidoqueen (but not Nidoking, so clearly they thought it was particularly appropriate to Nidoqueen for some reason), Slaking (!), Aggron (!!?), Maractus, Groudon, Armaldo, Bouffalant, Stoutland, Registeel (but not Regirock or Regice, so again they must have thought that this was an especially good move for Registeel in particular), Crustle (?), Ferrothorn (?!) and, of all things, Slowbro (but, once again for reasons beyond my comprehension, not Slowking, so someone must have thought at some point “what can we give Slowbro to emphasise the differences between him and Slowking? Oh; I know, AERIAL ACE.”).
