This video (from 8 min.53 sec.) shows that the verb recur is often pronounced as reoccur, and the host of the show explains this as a case of a mispronunciation: there's no such word as "reoccur" and what may be pronounced as "reoccur" should be pronounced as "recur".
It seems that either the speakers don't see any difference between the two verbs, or this difference is far too small to be taken into account.
At the same time, the entries for both reoccur and recur, and for the relating nouns recurrence and reoccurrence (the same links) can be found in some of the dictionaries; the WordWebPro off-line dictionary is among them.
The question is this:
If there is a fine difference in the use of the verbs recur and reoccur and of the nouns recurrence and reoccurrence, what is it?