Termux is just a terminal emulator. When you run programs in Termux they run natively on your Android system inside the normal Android sandbox of the Termux app. That has some limitations, for example software has to be compiled to use the paths of the Termux environment. Termux can't just install software into /bin and you can't write into /etc. So everything depending on anything more than the base Android system like dependencies installed by Termux has to be compiled specifically for the paths of the Termux environment. But it also advantages especially when you want a Terminal that is actually part of your Android system. You can just natively access the shared storage for everything Termux has permission to. You can also use the Android API out of Termux – for some things you need to install the Termux:API Addon app – and get stuff like GPS, SMS and contacts.
The Android Terminal app is just a view to a full VM. If you want a more traditional Linux system on your phone alongside Android instead of a Terminal in Android, essentially having a second system just conveniently running on the hardware of your phone, then that's for you. However it does also use more storage.