I have always been puzzled by this and I hope someone can help me. Thank you in advance.

When I write an essay sometimes someone I cite a source by saying something like, 'Jones (1980) said that X = Y.' But other times I say, 'Jones (1980) says that X = Y.'

Said or says? Which is correct? Or doesn't it make any difference? Once again, thank you. :)

Both are correct in US English.

In English, use the Present Tense; and don't use "says" - use 'Jones(1980) writes…'

Both are correct In American, because American doesn't have any fixed rules of grammar.