I don't think you quite understand. When it comes to character design, they're the same character:
As you can see, Captain Toad is a recolor of Toad with different clothes. They use the same character design.
But as far as being an individual, yes, you are correct. Captain Toad, Blue, Toad, and Yellow Toad are separate individual characters in the game's world/story. Just like Bandanna Dee and Sailor Dee are separate characters and
Red Yoshi, Blue Yoshi, and Yellow Yoshi are separate characters. Or Dark Link and Link.
Wut at the bolded. No, no they're not.
There is only
one defined individual Yoshi that is just a generic Yoshi in design, and that's "Yoshi" the Green Yoshi that serves as Mario's pal and sidekick.
Aside from that, you are the one who doesn't understand.
Design
doesn't matter. What
does matter is the individuality. Captain Toad is a defined character that has his own starring role spin-off game and is the Captain of the Toad Brigade, and Bandana Waddle Dee is a defined character that serves as the "elite" member of his species and is both Kirby's friend and Dedede's personal assistant/advisor.
Why would the generic counterparts of their species be added instead of the
major and defined individual characters? It's not like the Pokémon where they are representing the species as a whole, they're representing
themselves.
And if design
did matter....then we would never have Luigi in Smash, who's generally been a palette swap of Mario with very slight changes since his conception as a character.
Also, take Kirby. Recolor him navy blue with white eyes and purple feet. Give him gloves, shoulder pads, a cape, a sword, and a mask. Who do you have? Meta Knight.
But as we all know, those individual Yoshis are costumes for Green Yoshi in Smash along with Dark Link being a costume for Link. This is because they share the same character design irregardless if they're separate individuals in the games they hail from. As we can see in previous Smash installments, the original design is usually the default when it come to character designs.
....Those are all palette swaps.
Palette swaps of (in Yoshi's case) other generic Yoshis in colors of the species itself and (in Link's case) a living manifestation of the darkness inside Link.
Maybe the site doesn't say "only", but that's probably because it was not needed; it is quite obvious what it means.
Apparently not, because it means "Mii Fighters and Palutena are exceptions", not "Mii Fighters and Palutena are the only excpetions".