I can speak somewhat for at least the early Ayler, in that when Fontana bought the Debut catalog, they changed the artwork on some titles. Later, Polydor/Philips bought Fontana and yet again some changes were made upon issuing the material for other markets.
With respect to "My Name Is..." I believe that Fantasy leased the Fontana (nee Debut) recording for American distribution in the '60s, which probably stemmed from the strange relationship between Fantasy and Danish Debut (a fan-based label that originally licensed Mingus music in Denmark, though it became quite different a few years later). Fantasy and Musidisc/America were also in cahoots at that time, leading to the America pressing of "My Name Is Albert Ayler." America would have pressed the LP for France and Spain, Fontana/Philips for the UK and maybe Germany, and Fantasy for the US.
Bird Notes was a tiny vanity label owned by Swedish saxophonist Bengt "Frippe" Nordstrom; in addition to Something Different, he also issued a (mostly) solo album entitled Natural Music and a super-tiny run of a Frippe-Don Cherry duet recording. In fact, someone showed me a provenance listing of the Frippe-Cherry LP, with under ten copies in existence and all of their whereabouts known at the time! The Swedish label Sonet reissued the Ayler later in the '60s, and I assume they shared the rights with GNP. DIW put it out in Japan in the '80s, as they did with Sonny's Time Now and a few other rare free jazz titles.
This is to say nothing of the various bootlegs and leases of out-of-print material, which we all know is routinely messy and dubious.
I find the early pressing/cover variants pretty fascinating on a lot of things. The Prestige/New Jazz/Esquire scene is rather hip; maybe sidewinder can illuminate us on some of his interesting Esquire finds.