Mobile routers are mostly intended to be stationary and to provide network access via a mobile network, but do not need to have a battery. Example the new 5G routers, or the older "emergency/back-up 4G/3G GSM routers".
Mobile hotspots (aka MiFi) are mainly for mobile access on the go (trousers pocket/backpack). Always have a battery/battery so they can be operated "on the go". They access the same radio networks as mobile routers (3G, 4G, LTE, soon 5G). Mobile hotspots usually have a smaller processor, which is why only a handful (maybe 10) of users can connect via WiFi.

This device is therefore a mobile hotspot; however, it does not appear in this category ?!

it is the same. The router has only one data sim, which affects the cost depending on the provider.