Summing up from the comments:
First you need to understand that updating apps works different on Android than it does on a "normal" Linux distro: There is no such thing as "apt". Though Android has its own package manager (listening to the
pm command), installs/updates are usually dealt with by services/apps like google-play-store or other alternative-markets.
pm would rather be comparable with dpkg on Debian-based systems: it can do local installs (i.e. with the
.apk file already present on the device itself:
pm install would be the command for that), and a lot of other things.
Apart from that: a terminal app can be compared with a terminal on Linux allright. You get a text-mode "window" where you can execute commands. Most are even similar to those available on Linux, as Android is Linux based: you have things like
grep, and more. For details on this, you might wish to take a look at e.g.
- Ten basic Android terminal commands you should know (AndroidCentral)
- Using the terminal (XDA)
- Android Terminal Commands (XDA)
- Android Shell Command Reference (Github)
- our command-line tag-wiki
A look into our terminal tag-wiki will not hurt either :)
I'd say all terminal apps available for Android should support the above. Some even offer additional features, such as an entire development environment (Terminal IDE), or access to remote servers (JuiceSSH).