Haber y to have

Different IE roots. False cognates! ho dunnit? The Spanish grammarians did a bit of reform:

12th cent. Old Spanish aver. The spelling change from aver to haber was a modern modification to more closely reflect the original Latin.

They added a loop in the etymology tree.  But they wee likely influenced by English, by then, which was using something closer to 'habe' a German root.  Perhaps they go confused and, like me, at first thought they had the same root.  Nation forming has a strong written language component, so we see a lot of ancient etymologists changing skew in the tree, not necessarily to the worse.

The French compressed a lot of the old Latin and Americans inherited a bunch of the compressed forms. But they works fine, the Compression fit the newsprint fairly well. A bit of compression can reduce the dictionary size and maximize your literate audience.