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.

acquaintance is what you know, knowledge is like how wise you are.

Here are some examples of the usage of acquaintance and knowledge: Acquaintance -She ran into an old acquaintance at the grocery store. -Our family's close acquaintance with our neighbors -She struck up an acquaintance with a man from the city. -He seemed cold at first, but on closer acquaintance I realized that he was just shy. -While he has some acquaintance with the subject, he is not an expert. Knowledge -She has little knowledge of fashion. -He has devoted himself to the pursuit of knowledge. -She gained a thorough knowledge of local customs. -Did you have any knowledge of her intentions? For acquaintance the common meaning is a person whom one knows but who is not a particularly close friend. And for knowledge it is usually something you learn through experiences or education.