So now , depending how you count them and which sources you count, there are among 10-20 transformations/forms can attain. (counting Oozaru, non exclusive saiyan forms, etc.) Which saiyans transformations are the result of rage , which are the result of training and which are the result of something else?
- Super Saiyan: Any Saiyan with a sufficient amount of S-Cells and increase their battle power, they gain more S-Cells. Once the Saiyan attains enough S-Cells, a feeling of strong anger or sadness can trigger the Super Saiyan transformation. After the transformation is attained once, they can transform into it any time by focusing their energy into their back to make it tingle. Saiyans with a very high amount of S-Cells can do the transformation without requiring a trigger.
- Super Saiyan 2: There are multiple ways to attain this transformation. Firstly, a Saiyan must be strong enough to generate a lot more energy compared to the Super Saiyan form. The first way to attain this transformation is when the Saiyan experiences a powerful emotional upheaval, much like the Super Saiyan transformation, but to a greater extent. The second way is through harsh training. The third way is out of instinct from a desperate need such as when someone's life is at stake. Finally, the fourth method is for the Saiyan to feel out the tingly feeling in their back. The power output emitted by this form is greatly increased.
- Super Saiyan 3: This form is obtained generally after harsh training and usually under out of the norm circumstances. Goku was able to achieve this form while he was dead and training in the other world. Goten and Trunks managed to achieve it only during fusion. It's basically a transformation that increases the amount of ki utilised.
Important Fact: Akira Toriyama stated in the Saikyō Jump's June 2014 Interview that the SSJ2 and SSJ3 transformations are nothing more than powered up variants of the SSJ transformation. Hence you could potentially surpass the power of SSJ3 or SSJ2 while using the SSJ transformation by either training or through rage like in the case of Future Trunks and Vegeta. Although Trunks's Transformation is referred to as Super Saiyan Rage or Super Saiyan anger, it's basically a powered up variation of SSJ2 which was caused because of rage.
Hence to answer your question, there isn't necessarily a regular Super Saiyan transformation which can only be attained by either rage alone or training, it can be attained in both ways.
However, the Super Saiyan God transformation can only be attained via the ritual and not by anger. (Based of the manga), training vigorously with a Deity and practicing extensive Ki control could also help you attain this transformation as we see Vegeta use the same against Goku Black in the Manga. The Super Saiyan Blue, on the other hand, can also only be attained by training vigorously and absorbing the ki of a god and then transforming into a Super Saiyan. Super Saiyan Rose is basically the Super Saiyan Blue transformation when done by an actual deity (Zamasu). Apart from the God transformation, all the regular Super Saiyan transformations can be attained through training, rage or even when you are in a life or death situation. Based on the recent episode, we see Vegeta reach a level beyond Super Saiyan Blue without actual training but while feeling a strong urge to protect someone(Keep up his promise made to Cabba), which could be compared to Gohan attaining the SSJ2 transformation when Cell the Baby Cells were beating up the Z fighters. So if you possess God ki and can use the transformations, attaining a level beyond through rage and emotion like the Super Saiyan transformations seems plausible.
Almost every other transformation is explained by others, so I will just explain the oozaru and ultra instinct.
Oozaru : The Saiyans will turn into this giant ape if they look at anything that can reflect sunlight. Only Saiyans with a tale can undergo this transformation.
Ultra Instinct : It's not a Saiyan transformation. It is basically just like sage mode in Naruto.
- Oozaru: seeing the moon
- False Super Saiyan: getting mad, having a high power level
- Super Saiyan : getting mad , having a high power level (explained in the series)
- Super Saiyan 2: gettind mad , mastering super saiyan already , training (seen in the series)
- Super Saiyan 3: training and looking energy deep inside you (Goku's words)
- Super Saiyan 4: training for a high power level and having a saiyan tale, become a golden Oozaru and regain consciouness
- Super Saiyan Rage: having a high power level, mastering super saiyan 2, getting really mad, probably having some knowledge of god ki
- Super Saiyan Berserker: Being a special kind of saiyan who can get it and getting mad.
- Legendary Super Saiyan: Being able to regain consciouness after becoming Super Saiyan Berserker
- Super Saiyan God: ritual of 5 pure hearted saiyans surrounding a saiyan or internalizing this power
- Super Saiyan Blue: becoming a super saiyan after becomig a super saiyan god
- Super Saiyan Rose: becoming a super saiyan after being a god
- Beyond Super Saiyan Blue: Getting emotional after being a super saiyan blue, breaking a shell of power
- Ultra Instinct: breaking a shell of power, prolonged stress against a stronger opponent
- Golden Oozaru: turning super saiyan after becoming oozaru.
- Mystic form: power unleashed by the elder kai