Does it make any difference what spec ATF you use,yes it does. Even before synthetics it did.
My son in law had a full size Dodge Van that called for ATF+3. He has a leaking transmission and stopped at a store to get 2 quarts of transmission fluid. He didn’t find any ATF+3 on the shelves so he bought a generic dexron equivalent. The van didn’t quite make it a mile before it was slipping so badly it wouldn’t move but it was still full on the stick. I came and got him with 5 quarts of ATF+4 ,which had replaced ATF+3 , a drain pan , funnels and empty jugs , We drained and refilled the tranny and tightened the clamp on the neoprene line connecting the hard lines to the transmission cooler.
Problem solved.