There are three forms of continuing applications- Divisional, Continuation and Continuation-In-Part (CIP). It is important for a patentee to understand the difference between the three.
A divisional application is often filed as a result of a restriction requirement made by the examiner. The divisional application must claim the benefit of the prior nonprovisional application.
Continuation applications involve filing a patent application before the patenting or abandonment of or termination of proceedings on his or her earlier nonprovisional application, based on an earlier filed patent application wherein there is no new disclosure, but which may contain new or additional set of claims.
A "continuation-in-part" application ("CIP" or "CIP application") is one in which the applicant adds subject matter not disclosed in the parent, but repeats substantial portion of the parent's specification. A CIP is also filed before the patenting or abandonment of or termination of proceedings on his or her earlier nonprovisional application.
In all the three forms of continuing applications as understood from their brief descriptions, the claims or at least some of the claims may remain same as that of the parent (prior non provisional) application.
A divisional can be filed after a rejection requirement is issued by an Examiner, a continuation and a CIP however should be filed before the patenting or abandonment of or termination of proceedings on his or her earlier nonprovisional application. Hence a a continuation and a CIP cannot be filed after termination of proceedings (allowance of claims) or issue of patent for the parent application.
For further details on CIP applications you may visit the link, http://www.invntree.com/blogs/patent-protection-for-improvements-made-over-your-previously-filed-patent-application