I am pretty sure I'm not using the right terminology, but I'm trying to create the same effect in this image:
Is there any way to do this in Illustrator? What is the proper terminology for that effect? Any help would greatly be appreciated. I don't even know how to google that effect.
This is called 'extruding' an object. In illustrator, select your text and apply the Extrude & Bevel effect (Effect > 3D > Extrude & Bevel...). Check the 'preview' box and play around with the options in the dialogue box that appears to get the desired result.
You don't have to expand your text before applying the effect. This way, you can change the text after applying.