Yeah, if you want to do calisthenics then the best thing to do is to follow a calisthenics routine. Some yoga routines have a decent amount of calisthenics in them, many don't. Also, progression is going to be much better with a good calisthenics routine - most yoga routines and classes have a very poor sense of progression.

Same goes for stretching as well. A good stretching routine is going to get you much more flexible faster than doing yoga. Yoga has stretching in it, but again, it's unfocused and tends to have a very poor sense of progression.

Yoga is probably more akin to a sport. You can keep fit by playing sports, depending on how much work you put into it. But if you're trying to build strength, cardio, or flexibility, you're going to get much better results with a routine that focuses on those.

This actually isn’t necessarily true, one of the reasons I loved Sivananda yoga was that the classes were near identical and you could see yourself getting better at the breath hold/shoulder stand/sun salutations/etc. as the course progressed.