The two DisplayLink ports, marked HDMI 1 and 2, utilize a DisplayLink chip to extend displays using USB 3.0 data connectivity. This method of extending displays is typically used to add additional displays beyond the capabilities of a computer's built in graphics processor. The two DisplayLink connections do require that drivers be installed on the computer, and you can find a link to those drivers at the following address.
The two Alt Mode MST ports, marked HDMI 3 and 4, utilize a technology called Multi-Stream Transport using DisplayPort Alt Mode over a USB-C cable. This allows a single display signal, coming directly from the computer's Graphics Processor, to be split so that it can be displayed on two separate monitors. The end result of this lets you connect two 1080P displays and use them to extend your computer's desktop.
It should be noted that the resolution of these two displays depends on what version of DisplayPort your computer supports and requires a minimum of DisplayPort version 1.2.