TRM Modems
Like name implies is simply that, a modem to supply internet connection to already existing devices. Imagine USB stick modem just for industrial purposes with rugged housing that can be controlled through AT commands and provides wide range of connectivity options like 2G (EGPRS) to 4G LTE Cat 1, LTE Cat-M1 and NB-IoT
TRB Gateways
Much more functional than TRM modems, on top of simply providing internet connection, they can be controlled through RMS (Remote Management System) Depending on model they feature serial ports (RS485 and RS232) to connect to industrial devices, Inputs/Outputs, to connect sensors and device control, or RJ45 Ethernet port. They have GUI to connect, control and configure through browser and can establish VPN services for secure remote connection, Modbus, MQTT and other protocol for device control and data transfer.
RUT Routers
They have widest variety so it is hard to describe them in short. Depending on model one device can support wider variety and bigger number of devices connected, while featuring all previously mentioned capabilities and more, like GPS, multiple ways to connect to the internet (Wired WAN Mobile Connection WiFi Station mode), double sim cards for connection redundancy, they are simply much more universal than Modems and even Gateways.