Some providers don't seem to present a lot of information about what MiFi is, case in point, Cell-C. Stay classy Cell-C.
So after some cursory research, I discovered that MiFi isn't some new and speedy Wi-Fi like transmission protocol. It's literally just a Wi-Fi hotspot device. Mobile hotspot devices have been in play for a while now, In fact since they were invented and implemented in 2001. They gained traction around 2012 and became part of many peoples every day life. MiFi devices were pushed into the market around 2009. It turns out that MiFi is just some marketing branding to pull more users into the Mobile Wi-Fi market. It starts to make sense when you think about it from a branding perspective; "Mobile Wi-Fi" but the nomenclature is completely illogical from a technical standpoint.
Now many of us know how to tether to a mobile cellular device and use it as an internet access point. This works most of the time for most users, however there is little control over bandwidth usage, the host cannot control and monitor what users are doing and security can actually be an issue for the host and the users. Tethering is usually limited. Technically Tethering involves the use of a cable, Mobile hotspots being wireless.
Something cool about MiFi devices is that they usually have removable batteries. This means that if a battery gets low, you can swap it out and continue with your connection. MiFi devices also behave like WiFi routers, meaning you can control bandwidth, time windows and basic firewall rules. Unlike tethering or cellular mobile hotspots, these MiFi devices don't disconnect if the host device receives a GSM call or a text message (Source).
MiFi, improved tethering/mobile hotspots. Catchy name. Nothing new.

PiFi on the other hand...