Hi, CoreService is defined in JSR281 and it covers basic IMS functionality, like pageMessages and basic IMS calls: IMS sessions for streamed media and framed media.
IMService is handling instant message functionality according to the OMA SIMPLE IM 1.0 (@see ConferenceManager, FileTransferManager, ...).
JSR281 defines CoreService which enables an application to establish sessions and communicate with remote peers over the IMS network.
JSR325 extends the IMS functionality with three new services, PresenceService, XDMService, and IMService. These interfaces all extends the Service interface. This specification also makes use of the entire IMS package defined in JSR281, which was designed to be a common part for all IMS based enablers.
About registration, there is the method doRegistration from the class named RegisterServiceImpl, package: javax/microedition/ims/core/sipservice/register.
Hope this helps.