Hopefully this will clear it up once and for all.
There are two formats (regardless of file extension):
old MOBI
new MOBI
Additionally, you can combine both in one file (so an old device still reads the old MOBI, but a new device sees the new MOBI).
old MOBI has the file extension .mobi
new MOBI has the file extension .azw3 and is called AZW3 to distinguish it. It is a new format, and honestly, has about as much to do with old MOBI as EPUB has to CBZ -- that is, they both use the same compression wrapper.
You probably have Apprentice Alf's tools
which helpfully rename all files on import into the above-described
sensible distinguishing filetypes.
When does the confusion set in? Amazon -- they for some G-d-blessed reason name ALL ebooks, whether MOBI, AZW3, or for all I know, Print Replica, Topaz, etc. -- to plain old AZW (a filetype which strictly speaking does not exist, and certainly shouldn't). At least on the PC/Mac applications I believe -- while Kindle Fires get .prc instead, along the same lines of illogic.
To pile on additional confusion -- E-Ink Kindles get .azw files which are really MOBIs, and .azw3 files which are indeed AZW3 -- which actually makes a modicum of sense.
As though it mattered -- no Kindle app/device cares what the file extension is anyway, though you probably do care.
One final fun fact -- why are both called MOBI? Because they are in a way like EPUB2 and EPUB3 -- both called EPUB.
Technically old MOBI is mobi7 and new MOBI is mobi8 (KF8) -- the evolutionary form of the old mobipocket ebook format.
Read all about it in our Wiki -- if you dare.
MOBI AZW3