Amazon only has AZW and TOPAZ ebooks. AZW is the same thing as MOBI (extension .mobi or .prc), but it is always .azw when delivered from the Kindle Store.
The only method I know of to distinguish the two without downloading at least a sample is that TOPAZ ebooks don't list the
File Size on the ebook web page. This apparently isn't foolproof, but it is all we have. TOPAZ ebooks always have DRM.
AZW ebooks can come with or without DRM. If it was delivered to Amazon via mobipocket.com, then it always has DRM (because mobipocket.com does not handle DRM-free MOBIs). So if the same ebook is available at mobipocket.com (or any ebook store that only gets MOBIs from mobipocket.com) the odds are very high that the AZW has DRM. If it came to Amazon via DTP, then by default it has no DRM. However, it could still have DRM if the publisher/author uploaded a DRMed MOBI.
If you want to try to reverse engineer the DRM state, see
Kindle Books From Amazon Without DRM for a list of a few DRM-free AZWs. A search for "drmfree" at the Kindle Store also lists 12 hits. Here are a few TOPAZ ebooks: B000SB4MQY, B001AV4D4M, and B001E95MWC.