When it says egg moves, is that just the moves it can learn breeding but not leveling? But any move it can learn by leveling up it can learn through breeding?
yes a leveling up move can be an egg move if both parents know already the move for example you want a eevee to have bite (at least in gen 3) then you should breed it with a pokemon that already knows bite such as growlithe
Egg moves are special moves a Pokemon learns through breeding. But only the male Pokemon may pass down moves.
Take this Pikachu. As you can see, the move DoubleSlap is a move it an learn only through breeding, as it can't learn it from leveling up.
Hope This Helped :D