Toad is like Yoshi in that there is both "the" Toad (blue vest, red spots; SMB2, Wario's Woods, multiplayer Mario games) and a species called Toads (SMRPG, Paper Mario, Sunshine, Galaxy).
In the same way, there is both "the" Yoshi (adult and green; SMW (his house appears, and he's the first one Mario finds in a block), multiplayer Mario games, Smash, Tetris Attack, SM64) and a species called Yoshi(e)s (SMW, Yoshi's Island, Yoshi's Story, SMRPG, Paper Mario, et al).
It's unclear if characters like Koopa and Paratroopa as they appear in the multiplayer Mario games are intended to be "the" Koopa and Paratroopa as with Toad and Yoshi, but it at least seems to be the case.
EDIT: As to how this applies to Smash, Peach's shield Toad appears to be "the" Toad, with the red spots and blue vest (although this combination seems common, at least in Paper Mario). If he had been replaced with a Toadsworth or Toadette, perhaps, for the attack, Toad himself would likely have a chance as a playable character or at least an AT. As it stands, though, it doesn't look good for the little guy.