No, there is no difference.
Seem is a verb that governs infinitive complements and allows Negative-Raising. That means that negation in the infinitive complement of seem, or want, or other Neg-Raising verbs, as in
- The rule seems not to work. [ = ... to not work]
- He wants me not to go tomorrow. [ = ... to not go tomorrow.]
can also appear, instead, in the matrix clause with seem or want
- The rule doesn't seem to work.
- He doesn't want me to go tomorrow.
without a change in meaning.
This is not true of most predicates, which don't allow Neg-Raising. (Be) Easy, for instance, is a more normal predicate; the two sentences below do not mean the same thing.
- It's easy for him not to smile.
- It's not easy for him to smile.
Edit: Pursuant to RegDwight's comment above on split infinitives, I should mention that both the unsplit variant not to smile and the split variant to not smile are in the complement clause, i.e, not Neg-Raised -- though they are likewise equivalent in grammaticality and meaning. Either form can be regarded as the "source" of the Neg-Raised not easy to smile