I'm not sure what sort of yoga you practice, but if it is more based in Hinduism then this would be one of the major differences between it and Buddhism. [1] In all schools of Buddhism there is the teaching of anatman, that there is no self or soul. [2] So the attitude around 'I' is a bit different, mainly that there is no permanent 'I' to identify with. Still, you're right in that 'I am a body' isn't quite right either.

[1] There are Buddhist yogas though, mainly from modern day Bangladesh that were preserved in Tibet, for instance https://en.wikipedia.org/wiki/Six_Dharmas_of_Naropa and the trul khor exercises. A Baul I've been lucky to practice with a little talks about it too: https://www.youtube.com/watch?v=7JZ4__GTbjA

[2] https://en.wikipedia.org/wiki/Anatt%C4%81

One way that I sometimes think about this is that we are all of these things, and that being one thing need not preclude being another as well.

Breaking the identification is a big part of Yoga from my experience.

But so is being fully within your body and not fighting it.

As well as disciplining it and removing any disturbances.