Small correction: Visual Studio does not keep track of the project template used to create a project. The project system is largely unaware of the initial template used for a project. There are several items in the project system (Project Type for instance) which have the same name as specific templates but this is a coincidence and the two are not definitively corrected.
The only thing that can really be changed in terms of the project type is essentially the output type. This can have value Class Library, Console Application and Windows Application. You can change this by going to the project property page (right click Properties) and change the Output Type combo box.
It is possible to have other project types supported by the project system but they are fairly few and are not definitively associated with a project template.