While Winged Goomba shares similar traits as its not round counterpart, there are many reasons that does not crown it as a normal Paragoomba:
It is a winged variation of Super Mario World round version of Goomba (whose name was spelled as Kuribon in Japan as opposed to the normal Kuribo), this enemy when is stomped, it will simply flip over (instead of getting squashed) allowing Mario (or Luigi) to pick it up like a Koopa shell.
It seems to be unable to fly, as it can only do small hops.
When the enemies' cast is rolling at the end of Super Mario World, the name Para-Goomba (note the hyphen), was, in fact, used for the same round variation of Goombas who utilized parachutes to descend.
In Super Smash Flash
Winged Goombas are the second most prominent enemies, with Koopas being the first, to appear in the stage Super Mario World. Their attack pattern is the same to all the airborn enemies in SSF, such as Beeleys or Buzzers; it has to make collision with the player in order to damge him. They are very weak enemies as one single attack is enough to get rid of them. A very notable difference between Winged Goombas found in SMW and Winged Goombas found in SSF is that Winged Goombas in SSF will not lose their wings if there are stomped, or more specific, attacked; unlike those in SMW. Also in SSF, Winged Goombas are able to fly freely while in SMW the only thing they did was make small hops.
Winged Goomba is the only enemy in SSF to have a custom animation. When it is defeat, a Winged Goomba with cross-shaped eyes can be seen.