Do the following negations mean the same thing?

Solution 1:

Think is one of the verbs that govern the rule called Negative Raising.

Nothing actually gets raised, though. What this means is that the verb think is transparent to negation, because it doesn't really mean anything except to identify what you're thinking about.

Consequently
- X think (not Y)
is equivalent to
- X not think (Y)

Other predicates that govern Neg-Raising include believe, feel, appear, intend, expect, seem, and suppose. These are all verbs of mental state that take complements.

This is not true, however, with most verbs that take complements.
Neg-Raising is a minor governed rule, with relatively few verbs that govern it.

• I said he didn't like it. ≠ I didn't say he liked it.
• She tried not to smile. ≠ She didn't try to smile.

Solution 2:

They are very close, and may be used to mean the same thing, but there is a semantic difference between not understanding and misunderstanding.

If my wife calls to me from the TV room and I can't understand what she says (i.e. I can't quite parse the meaning because the sound doesn't reach my ears intelligibly enough), then I have not understood. However, if I hear she wants me to bring her a fork, but she wanted some pork, then I have misunderstood.