1: Harry was supposed to become an earl
It was intended that Harry should become an earl
This is a special use of the verb to suppose that only occurs in passive contexts (where the actual "agent" doing the "supposing" is unspecified). But hopefully you can see how the more common meaning to suppose = assume / think / guess stretches through to expect to anticipate / plan for / intend [that something will happen, or be true].
2: Harry was thought to become an earl
...doesn't really make sense at the semantic level, but if we change become to plain be it would mean that (unspecified) people believed / were under the impression that Harry actually was an earl. Note that exactly the same substitution wouldn't make any difference to the meaning of the supposed version as given above.
EDIT: I just realized there are perfectly ordinary contexts where the superficially "unusual" syntactic structure in #2 above is unexceptional. For example...
3: Hay lying on the ground was thought to become poisonous
4: ...men were thought to become wolves
5: ...patients were thought to become unnecessarily institutionalized
So perhaps Harry was a fervent socialist who claimed that he always adopted a free "peasant" persona when playing online games set in medieval Arthurian England. Peasants would be at a disadvantage in those games, because they'd have limited resources, but players could pay for a more powerful persona (a squire or a knight, for example). Harry boasted that even though he could afford to pay, he was virtuously "handicapping" himself to show solidarity with the working classes throughout the ages. But some of his friends suspected Harry was lying, and that he didn't become a peasant in the virtual world. In fact, Harry was thought to become an earl (some thought maybe he even paid enough to become King Arthur himself! :)