How many kinds of yoga are there?

Just one kind! "Bodybuilding Yoga" is called yoga pose. "Breathing regulation" refers to yoga breathing control. You may understand "controlling emotions" as psychology or theory. There are many other contents. Unification is called yoga.

For example, an apple tree has its roots, stems, leaves, flowers/fruits and so on. They formed an apple tree. For example, if you take out the "leaf" alone, it is a part of the apple tree, not a kind of apple tree.

Alas, the answer downstairs is "wisdom yoga, career yoga, faith yoga, hatha yoga, Raja yoga, Kundalini yoga".

These are called branches, not categories!