.MOBI is a file extension/format supported by Amazon Kindle eBook readers. It is deprecated and has been superseded by .AZW
Mobipocket is an ebook reader format originally developed for the Mobipocket Reader software, introduced to several PDAs around the year 2000. The company behind it was acquired by Amazon in 2005, which then used the format for their own Kindle devices (which are still capable of reading it). The original software more or less died, and Amazon renamed the format to AZW (which is identically to Mobipocket with DRM protection). Further development was done on that, resulting in a.o. KF8 (or "AZW3") in 2011 and KFX ("Kindle Format 10") in 2015.
Mobipocket files usually go by the file extension
.mobi, but for PDAs also often used