Two things helped me wrap my head around this game.
The first is to re-map the controls. On the GC controller I did this:
A - Normal Attack
B - Special Attack
X - Grab
Y - Jump
Z - Shield
I also disabled the ability to tap up to jump.
This way, I can do Up-A, Up-B, or Up-Smash while standing without the game thinking that I’m going for short hop >> neutral A or something else random. Anytime I don’t get what I think I pressed, it would frustrate me, which is why I moved shield to the z button instead of it being on one of the analog buttons.
So, once you remap your controls so that you don’t feel like you are mashing, and you are getting your character to do exactly what you are inputting, you can put it in street fighter terms.
Tilt Attacks = Jab
Special Attacks = Strong
Smash Attacks = Fierce
As for the lingo, most of the terms are actually in the manual that came with the game.
The second important thing to understand is that there is no life bar. The point of the game is to knock a player off the stage. The higher the damage percentage your character has, the further back an attack will knock you out of ring. The amount of knockback distance is determined by the total amount of damage done by the combo that you landed, modified by the percentage that the character has already sustained. If the character already has 100% or more damage a high damage tilt attack can sometimes knock a character out of the stage just like a combo into smash would.
So, basically, learn how to combo into smash.