What is the difference between coreference resolution and anaphora resolution?

The answer by Tim Osborne is very comprehensive and accurate. But perhaps things might be easier when looked at through usage in text linguistics.

Although, co-reference and anaphora can be distinct, they are often used interchangeably by linguists. This is partly because by far the most studied type of anaphoric reference is co-referential. So you could say that co-reference is one of the processes through which anaphora is encoded. It is not just a type of anaphora because co-reference can also be cataphoric (although some people use anaphora to mean reference in both directions).

So the difference between anaphora and correference resolution follows from the above.