A Real Terminal (Root or No-Root) I use KUBUNTU on my laptop, but this goes for any Linux distro. I can open a terminal window and type in things like sudo apt-get update, sudo apt-get install packagename. Is there a terminal that can carry out commands like this on Android? It doesn't have to be "sudo", I simply mean carrying out commands. I use the Galaxy S3, but I doubt it really matter for the question I'm asking.
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 cd, ls, 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).