Xamarin's Lluis Sanchez Gual clarified the IDE situation on their mailing list. Xamarin Studio is in fact MonoDevelop, with the distinguishing factor being just a set of add-ins. These add-ins add in the support for handling Android and iOS projects plus Xamarin service integration such as with their new Component Store.
So at its heart, Xamarin Studio is still very much MonoDevelop just with some extras tacked on. Lluis went on to say in his mailing list message, "The development of MonoDevelop will continue like it has been in the past. All the improvements which are not related to Xamarin's commercial offerings will be done in MonoDevelop, and we have plans for a lot of them: code analysis, version control, debugger, etc. We are committed to keep evolving MonoDevelop, because a better MonoDevelop means a better Xamarin Studio."
Supporting Linux though isn't a primary goal by Xamarin developers but will continue to be supported. "MonoDevelop will also keep working on Linux. There may be some rough edges with MonoDevelop 4.0 on Linux, since for this release we put our focus on Mac and Windows, since that's what Xamarin's customers use."
MonoDevelop continues to be hosted on GitHub and the new code activity does keep coming in on a very frequent basis. This upstream MonoDevelop work is going into its forthcoming v4.0 release.