CMS 2002 supports both ASP and ASP.NET templates. If you install a clean copy of CMS 2002, you'll be asked whether you want CMS to support mixed mode; essentially, you'll need to instruct setup whether you want to support both ASP- and ASP.NET-based templates, or just the ASP.NET-based templates. In the case of an upgrade, CMS does not give you a choice; once you have finished your upgrade process, you'll be running in mixed mode.
Running in mixed mode is very much like running mixed verses "native" mode in Windows 2000, in the sense that you are supporting two different architectures. In the case of Windows 2000, you were (or are) supporting both Domain security and pure Active Directory. In the case of CMS 2002, you are supporting both ASP 3.0 and ASP.NET (all the files to support both are installed as part of running in mixed mode). In your converted templates, you will still see the old Autosession object, along with other elements such as Channels and Postings. There are some differences between the 2002 COM API and the 2001 version (most notably the way placeholders and the edit console are handled), but there is little material difference.
NOTE: There is really no way to take your server out of mixed mode. During the installation process, all the files necessary to support both ASP.NET and ASP templates were installed. If you want a "clean" CMS 2002 installation, you will have to create an export package, copy off your project, reinstall the server on a clean database, copy your project back, and import the CMS package you made earlier.