Always work in progress. "Work in process" would be a malapropism (getting similar sounding words in a phrase mixed up, like saying "chester drawers" instead of "chest of drawers"). Work in process is more to be used for goods/inventory/items that need to be processed rather than projects that need to be finished.
Native English speaker here, and I don't believe in 30+ years I have ever heard "process" used in this way. It actually sounds odd to me. I can see how some might use it, because being "in process" could mean that it's being created? I dunno, it just sounds weird.
It might not be wrong, it just doesn't seem right to me as a native speaker. I have been wrong about these things in the past, I am willing to admit ignorance, but try to correct myself when I find my mistakes.
They're both correct uses if you look it up on a thing that's called Google, even though I've only heard Work In Progress.
And if you look even further, they're NOT the same in artworks:
"Sometimes, outside of a production and construction context "Work in process" is used erroneously where the status "Work in Progress" would be correctly used to describe more broadly work that is not yet a final product."