I would say that when you become "acquainted" with a subject, you know just a little bit about it. Knowledge is more than acquaintance. It is larger and deeper. For example, you can say you are acquainted with modern art if you visit a couple of modern art museums. You can say you have good knowledge of modern art if you spend a couple of years studying for a Masters degree in art.
The word "acquaintance" can also be used to talk about someone, perhaps a friend of a friend, who you have met only once or twice. You have met them, but you do not know them very well.