Ce and ça both mean the same thing (this) in French, so what is the difference between them? When would someone use one over the other?
This answer will be about the pronouns, but note that ce -- cet, cette -- is also a demonstrative adjective and as such will be followed by a noun and that ça should not be confused with çà which is an old synonym of ici.
Ça is an alternative form of cela; they can replace each other in most if not all contexts, but ça tend to be used more often (but not exclusively) when speaking, while cela tend to be used more often (but not exclusively) in writing. One case where cela is used more often both orally and in writing is when it is opposed with ceci.
Ce, ceci, cela and ça are the neutral demonstrative pronouns. They don't replace a noun (forms with celui, celle, ceux, celles are used in those cases) but something implied or (part of) a sentence.
When they are opposed, ceci is used for the nearer (in space, in time or in the discourse), cela (or sometimes ça) for the further. Alone, ceci is for something quite near and cela or ça for something quite far, but cela is also used for things near, especially for part of sentences which precedes the pronoun.
Usages of ce are more limited:
and it is sometimes replaced with ça for emphasis.
« il / elle est » becomes « c’est » and « ils / elles sont » becomes « ce sont » IF - an article is followed by a modified noun.
« Ça » is an informal use of this and that as I know of. :)