Hmm best way to explain. First thing is to mention this is all my own thoughts on the matter so is easily up for debate.
That out of the way it's not so much that there is different kinds of telekinesis, that's a different conversation, but more that there are different rankings of Telekinesis. 

Basic Telekinesis is lifting/moving things with thought, the strength can be exceptionally high or low without leaving basic telekinesis. You can barely lift a pencil to you can lift skyscrapers, either way basic.

Advanced Telekinesis is when you start adding telekinetic properties to things. Object A pulls on Object B, or Object C repels all things near by, or creating fields or areas of telekinetic effect. 

Beyond that you start getting into esoteric things. Like condensing telekinetic force into a useable energy source, or creating slip space pockets of telekinesis to teleport.

From my interpretation of how Jinny went up the wall she didn't use basic Telekinesis. As that would simply be her grabbing herself with TK and pulling herself up no need for outside help to move. No, what Jinny did was encapsulate herself in a bubble of TK that followed two rules; push against gravity, and push against everything not in the bubble.

Useable for flight, if tweaked, but also allows for a lot of other applications. Invert the rules and put it on someone else and suddenly they are moving slower and have a much harder, if not impossible, time dodging those throwing knives she just picked up. plus if she can make TK fields she can add them as edged fields to her knives to make them sharper, or simply throw pointed TK fields to stab things with her mind.

Most TK only do blunt force, ranged punches or kicks. Jinny might be able to do mind bullets or saws.