Hypergeometric test equivalent for difference between two sets of genes list instead of intersection

Question

[Ivan]

It's common enough to do a hypergeometric test for the intersection of two gene lists to see if there's any greater-than-chance statistical overlap between two lists. For example, this post here or this online-tool here.

But suppose I want to test the difference between the two lists, rather than intersection. So instead of all intersecting elements of the two gene list, I do union minus intersecting elements.

Is there an equivalent of the hypergeometric test I can do for the (union minus intersection)?

[rpolicastro]

What hypothesis are you trying to test, or the null hypothesis you are testing against?

[Ivan]

Let's say that process 1 generates first list of genes and that process 2 generates second list of genes. I want to check if those two processes generate two different list of genes.