I've always referred to, as do the programmers around me that work on it, a mainframe being our IBM iSeries. A main server (we have 2) with remote stations connecting to it as terminals. In our environment, the remote terminals are Windows XP Embedded thin clients running IBM iSeries Access and the programming language used on the iSeries is RPG.
From the very little I understand, it ships with more processors than we use (CPU on demand) - jobs can be batched and assigned a priority. This is a the typical green screen banks use, although we use all 16 colors to make things easier to read and we have some mouse click functionality in the screen.
We're in the process of migrating to a new one, that came in its own IBM branded rack (the old one was just a standing floor model).
iSeries Access is just a glorified telnet program (I've connected to it over telnet via my Mac) and my website connects to it via ODBC. Aside from iSeries Access (being a windows program) there is no GUI. Its all what looks like a command prompt. iSeries Navigator exists, but we don't use it (this would be the closest to a GUI that we have)
I've worked for 2 banks in the past and they all used some form of machine like this from IBM. Before we purchased this new rack, we considered moving to a blade system but that would have required much more migration time than we liked. Our iSeries admin ust to work for a casino and they had an entire room dedicated to multiple rack systems. In our industry, there is 1 other competitor, and its Intel based. Our application is written in house and was written for IBM and RPG.
The "i" is a class - theres are others; zSeries comes to mind.