Is MIUI just another version of CYanogen Mod? 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.[6] Xiaomi added a number of apps to enhance the basic framework; those include Notes, Backup, Music, and Gallery.[7]

Updates are usually provided over-the-air every Friday.[8] 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.[9]

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.
As far as I can tell MIUI is a ROM developed by Xiaomi Inc and was designed to mimic iOS more than other android ROMs. It has been available to install on many devices for a while as well as for their own brand of high end Chinese Android devices (http://www.mi.com/en/).

As far as I know, its only relation to CyanogenMod is that MIUI used the core backbone of CyanogenMod to build upon in creating its own ROM and so will share some commonalities/similarities but they have always been available separately and often compared to each other as 'competition' choices with people favouring one of the other for their differences in overall design in the end product.