At 2nd job you choose between going for the light branch or dark branch skill tree. Light branch improves upon her 1st job and focuses more on ranged attack and supportive ability whereas dark branch is a melee combo powerhouse and is like playing a completely different character (but you can still change your passives around so you can use the 1st job combos if you prefer). Dark branch also loses her talismans/card whatever system completely in favor of a kind of fury bar that increases damage + gives life steal on attacks. She also has a few debuffs like curse.
3rd job further improves the branching skill trees.
4th job gives both branches access to the same 4th job skill tree, but the skills themselves are different depending on which branch you picked at 2nd job.
The video in first post actually shows quite a lot from the 2nd job and 3rd job combos too, just missing the MP skills from said jobs.
When they released her 2nd job they also converted her to a AMP character like Asin and Lime and made her 1st job skill tree like theirs in which you need to progress the skill tree to unlock parts of her combos and skills (lol KoG so lazy). 2nd job onwards is completely new content though.