On their wiki page:
The original MIUI ROMs were based on Android 2.2.x Froyo and CyanogenMod 6 sources, and was initially developed in the Chinese language by Chinese startup Xiaomi Tech. Xiaomi added a number of apps to enhance the basic framework; those include Notes, Backup, Music, and Gallery.
Updates are usually provided over-the-air every Friday. MIUI is then translated and ported into unofficial versions in other languages by independent developers and groups of fansites. The list of supported devices may or may not be complete, and ROMs are very similar but not identical. The list of fansites can be found on MIUI's official English website.
I was just having a discussion about MIUI with a friend. I believe MIUI is just another version of CyanogenMod. Is this correct as there are various conflicting pieces of information scattered on the internet.
NOTE: I am not sure if this is the right place to ask this question, please let me know and I will migrate this question.