It's quite a bit more complex than that. These are terms from different historical periods. In pre-petrine times, there was only "tsarevitch", and it did indeed mean "son of tsar". Then there came Peter and changed his title to "Imperator", which necessitated new titles for his family, and so his daughters got a new title "tsesarevna", which is the female form if tsesarevitch (he had no living legitimate sons at that point). And "tsarevitch" officially stopped being a thing (It still was used informally, though.) Which members of imperial family got the right to be titled "tsesarevitch" flip-flopped a bit until in 1797 Pavel the First decreed that it was to be the title of the heir to the throne, and that decree persisted until the end of the empire. Even if Pavel broke it just two years later by awarding the title to his second son as well as the first.
So, initially "tsesarevitch" was literally "tsarevitch, but westernised a bit", and that shows in the spelling. It was never intended to mean a different thing, only to supplant the earlier term.