In terms of normal meaning, there isn't a difference. However, the two can be interpreted as having different grammatical nuances, and they aren't completely interchangeable.
When I hear not educated (and it may be different for others), it conveys to me a sense of having received no education in the past. But when I hear uneducated it seems to be more related to a present state only. In other words, while they both do refer to somebody's current level of education, I personally think of their past more with not educated than I do with uneducated. This may just be me, and it's possible that others don't perceive such a subtle distinction.
This might have to do with the difference between these two sentences:
He has not been educated.
→ Nobody has ever given him an education.
He has been uneducated.
→ (1) At times in the past, he has been without an education.
→ (2) He has had his education removed from him. (Brainwashing, for example.)
While it's possible to say both of these, the second sentence, regardless of its interpretation, means something different than the first sentence.
Also, consider the following sentences:
✔ She is speaking in an uneducated way.
✘ She is speaking in a not educated way.
It's possible I could come up with an argument for why the second is not actually invalid from a purely syntactic point of view. However, it's certainly unidiomatic, and common usage would make the first the far more common.
In terms of grammar, uneducated is a more natural adjective than is not educated. While not educated is certainly used adjectivally, it's not done so naturally in constructions such as this.