Vegito powering up to become a super saiyan against buu

Super Saiyan
(超サイヤ人, Sūpā Saiya-jin) is an advanced transformation assumed by extraordinarily adept members of the Saiyan race in the Dragon Ball franchise, as well as Akira Toriyama's Dragon Ball parody manga, Neko Majin. Three further transformations succeed

This is Gogeta nad Vegito as super saiyans (you can see the difference in the super saiyan form)

Super Saiyan (two in manga canonicity), and the premier Super Saiyan form has three additional branch states.

These are Super Saiyans as they apear in the Majin buu saga and sub sagas (note that future trunks is there but is not in majin buu saga)

There are also two totally different types of Super Saiyan that appear in the films (the False Super Saiyan and Legendary Super Saiyan).
Goku SSJ Namek by shadsonic2-1-

This is a super saiyan