Overregularization and hypercorrection both result from analogy, but they occur in different contexts.
Overregularization is common in children's speech when they use regular forms for irregular verbs, such as saying "eated" rather than "ate." So a case of over regularization results from the improper extension of a successfully acquired rule that is part of the speaker's original internalized grammar.
Hypercorrection occurs when a speaker is aware of some feature or structure that is part of "prestigious" or formally taught language, but doesn't learn the formal rule governing its use and uses some other rule as a substitute (for example, using "whom" in the sentence "I don't know whom told you that"). So a case of hypercorrection results from the application of an unsuccessfully acquired rule that is not part of the speaker's original internalized grammar.