The difference between super saiyan 1 and super saiyan 2

Super Saiyan 2
In Super Saiyan 2 mode The golden hair brought on by the original transformation becomes longer and rigid and stands up even more. the aura now looks like a jagged fierce flame like appearence rather than being smooth or flowing.In most of the video games the electrical a lot of them normally blue but gold in Dragon Ball Z: Budokai 3 surrounding the body especially when they charge up. Not always present especially in the anime Gohan and Vegeta lack the trait in some episodes and sometimes look like a charging Super Saiyan like Vegito.
Legendary Super Saiyan mode
Legendary Super Saiyan hair is a greenish-yellow color in this form. Broly's pupils and irises vanish which make him look more maniacal than he already the most recognized difference between legendary super saiyan and regular super saiyan is the body size when Broly transforms his body grows in height and his muscle mass increases a lot making it similar to the Ultra Super Saiyan Transformation but unlike that mode his size does not affect his speed. His skin also becomes very pale in that color.
Super Saiyan 1
Ultra Super Saiyan is the third stage in the super saiyan mode and the second advanced branch is super Saiyans form this form is similar to the legendary super saiyan form. The skin of Saiyans in this form may become slightly reeder do to an increase in blood flow and muscle size is increased to the point of impracticality. there hair grows and spread in different directions. The aura does't flow upward but flails outward with surges of bio-electricity being more frequent and prominent. A few times the pupils and irises may vanish temporarily during transformation.

Ascended Super Saiyan this stage is similar to super saiyan with a few differences the flowing golden hair is slightly more rigid and pales in color muscle mass increases heavily but not so much. Thanks to the increase in muscle mass the Saiyan's outfit will end up tearing apart like when trunks transformed while fighting Broly and his jacket ended up being torn to shreds. The aura increases in size and becomes more jagged with bio-electrical discharge during transformation or when preparing a big attack like Final Flash. The aggressive remorseless behavior of the first form is increased. control of emotion is lessened because of the increased of the super saiyan transformation and more energy is required to keep this body in this form than in the regular Super Saiyan mode.

Super Saiyan while in this mode the users physical change is not too drastic apart from a small change in muscle mass their power is increased by a huge amount this transformation has a huge effect on the Saiyan's personality they become ruthless and are overcome with rage but when they transform to a super saiyan 2 they start becoming more experienced in this stage. Their most notable difference is that their hair turns golden in color and starts standing to an end giving it a rising flame like appearance this applies to all their hair including scalp hair eyebrows and the furs on their tails. Their eye color changes to a greenish-blue color muscle tones becomes more defined skin tone and clothing becomes lighter due to the energy and light output of the golden aura. As the natural floodgates of the body are opened with the transformation, excess energy is radiated from the body in the form of a pulsing, flame-like aura.There's also a change in personality where the Saiyans become more aggressive and more prone to acting on impulse.when in Super Saiyan their eyes are fully outlined to show the anger and hatred present at that form.

Full-power Super Saiyan is when a saiyan master the super Saiyan form it is debatable if there is any difference between this form and the regular super Saiyan form most of the difference can be because of Akira Toriyama's changes in artwork as the show continued the only confirmed differences is that the Saiyan's facial features exhibit less tension and ferocity than the regular super saiyan mode the aura is a bit difference but that might just be a mistake it appears less violent then ultra and ascended super saiyan mode when relaxed their hair is more of a yellowish white but when they power up the golden glow seen most of the times in the original transformation appears.

The terms "Ascended Super Saiyan" and "Ultra Super Saiyan" are actually just common fan terms to differentiate between the two bulked up forms, as they are never named in the manga or anime. However, they are named in the Daizenshuu books as Types or Grades 2 and 3.

If you would like to see their difference of strenght then go click this link https://animefanclub.forumotion.com/t13-saiyan-strenght it has most of them there except full power and legendary super saiyan mode

Gohan was the first creature who had saiyan blood to turn to super saiyan 2 he turned during the cell saga while the others did not get that mode yet and probably got it during the years that took place between the cell saga and Majin Buu saga. Vegeta was able to turn ultra super saiyan during the cell saga but did not since it would slow him down he knew that is what would happen so he never went ultra super saiyan and broly was the first and only full blooded saiyan to turn into legendary saiyan mode