It's a completely arbitrary semantic distinction that only exists because BECMI did things a bit differently than AD&D. It should have been reconciled in 2e when they converted Mystara to AD&D, but it wasn't. I recommend you utterly scrap it and consider them to be the same thing.
I wouldn't say completely arbitrary.
Many "Immortals" were originally mortal, and gained power through their task and dedication to a sphere.
"Gods" are more like pervasive created the universe type beings in other campaigns.
There are exceptions of course, but I always felt this was the distinction from Basic.