A comment on this question of mine alerted me to the difference.
Is this a case of the linguistic equivalent of "convergent evolution"? I don't see how that can happen with two languages as closely linked as Russian and Ukrainian.
Well, IMHO meanings of питати and пытать can be considered as relatively close. Although in most Slavic languages питати and similar words really mean something like “to ask”, but there are nuances:
I consider first two entries in the above list to be approximately the same: simply the word got meaning of something like polite plea/supplication in some languages/dialects and of hard high-pressure interrogation in others; except that meaning in Russian was then somehow shifted to tortures (personally I suppose either “check” → “test/temptation (Christianity)” → “mental anguish/tortures” → “any tortures”, or “question” → “interrogation with tortures” → “tortures of any kind” path — though I don't have enough competence to make such assumptions reliably). It is not uncommon for Slavic languages to have diverging meanings for similar/cognate words, e.g. Russian вонь means “stink”/“stench” while Czech vůně means “fragrance” (pleasant sensation) or “smell” (neutral word).
Both Ukrainian питати and Russian пытать certainly derive from same origin (see Proto-Slavic *pytati). Modern usage of the root пит:
P.S.: No, I'd not call it “convergent evolution”. Convergent evolution — that's when some things with different natures/origins get similar traits due to influence of somewhat similar environments. I'd better say “convergent evolution” for Ukrainian питати and Russian питать (“to feed”); or for Ukrainian керувати and кермувати. While in the case you've asked about it looks more like fork/divergence of Old East Slavic word.