Enable Developper Options. It should be in the Developer menu. It's a toggle that'll enable this apk.
Termux is doing a container. The android terminal is doing a virtual machine. That's the difference.
Termux would definitely be the light weight option, but you will be pinned to whatever version of the kernel your device is shipped with (may be a bit old.)
That doesn't matter much for using SSH though.
For running more complex Linux programs or scripts Termux is indeed less comfortable (but it can still work).