You can remap the controls. I immediately changed the jump buttons to Y and B and my light and heavy attacks to A and X on my 360 controller to match what feels natural to me playing Smash on a standard four-button layout.
Light and heavy attacks are like normals and specials in Smash. Since many characters share the same weapons, they have a lot of common light and aerial moves with them (but not all). Their grounded heavies are where the big differences lie. Every character has a unique combination of two weapons, from swords, lances, bows, guns etc. and they all have more or less the same moveset unarmed, so how each one is truly unique will come from their kill moves and how to set them up, as well as strategically throwing your weapon and picking up the other...
It makes more sense in practice than talking about it