Didn't Clarke even once say that he considered each of the books in the 2001 series as separate from the others, in its own little universe, with no concern towards continuity between books except in the major strokes?
Oh, yes. While many of his peers tended to tie their books and stories together into larger, integrated universes, Clarke went in the opposite direction; almost everything he wrote was a complete standalone in a separate reality from everything else. The only ongoing series he ever did was the
Tales from the White Hart series of short stories, about a fellow named Harry Purvis who told a series of almost-but-not-quite-plausible scientific tall tales to his fellow patrons of the White Hart tavern -- but since every one of those tales was (almost certainly) a lie, that barely even counts as a continuity. The
2001 sequels were the first sequel novels he ever did, and
2010 was a sequel to the movie version of
2001 rather than the book version. So it's no surprise that he approached the other "sequels" more as variations on a theme than as installments in a unified continuity.
There are a couple of later series that were credited to Clarke in collaboration with other authors -- the Rama sequels with Gentry Lee and the
Time Odyssey trilogy with Stephen Baxter. But the Rama sequels were really written almost entirely by Lee with Clarke just contributing some ideas and notes (which is why they totally suck), and I think the same must be true of
A Time Odyssey, given that it was written not long before his death. There's also
Beyond the Fall of Night, which is credited to Clarke and Gregory Benford, but I gather it's really just a fixup of Clarke's first novel
Against the Fall of Night and a continuation entirely by Benford.