Here's a 100,000 foot view of mainframes (based on when I was working with them and on my limited view).
The mainframes that I worked with (not sure if this is true with all) had something called Capacity Upgrade on Demand. This allowed the data center to temporarily turn on extra processors/engines to handle unusually high processing demands. After the crunch is over, the extra processors can be turned off. I'm not sure how the money aspect of this works.
What the x86 world thinks of as a bare-metal box/chassis is what looks like a full sized rack, except it's enclosed in a cabinet. This bare-metal box is carved up into LPARs (logical partitions) using software called PR/SM [1]. I've read a number of times that PR/SM is a stripped-down version of z/VM. I don't know if that's true or not.
IBM has multiple operating systems for mainframes. The most well known is z/OS (formerly known as MVS). There are others like z/TPF and z/VSE (maybe even more?). There is also z/VM.
JCL (Job Control Language) is used by z/OS (possibly z/VSE too, idk) for running "jobs". This is essentially like shell scripts. The job is submitted and then queued for execution. After execution, the results are made available in an output queue. From Linux on x86 point of view, it's like all program output is being redirected to a file.
There are a number of z/OS add-ons that are typically licensed to run on z/OS. One is TSO (Time Sharing Option). I don't know if TSO is separately licensed or not. Basically, it makes a batch environment almost appear to be interactive. Another component commonly licensed is ISPF (I don't know what it stands for). ISPF is basically a menu-based system that is configurable and I think it comes with some helpful built-in utilities.
z/VM's history goes back to the late 60's and early 70's. Supposedly, one of the primary reasons it was developed was to give z/OS system programmers a sandbox for developing and testing changes. Apparently, some mainframe shops also ran MVS and other operating systems as guests under VM in production (this was probably in 80's). This wasn't the only use of VM though. There was CMS that is a single-user OS that was typically used for end-user business users. Since VM with CMS guests were so common, one would often just see "VM/CMS" written. From within CMS, one could issue CMS commands as well as CP commands. CP is "Control Program" and refers to base z/VM (hypervisor).
One can also run z/VM as a guest under z/VM. This is referred to as 2nd-level VM and is used for testing/evaluating new versions of z/VM before installing them into production.
When Linux hit the scene, versions of Linux were built for mainframes and Linux was added to the list of guest OSs that z/VM supported. To be clear, this is real Linux -- not emulated. It's normal Linux, but compiled to mainframe opcodes.
Once you get access to a Linux guest on z/VM, it's really hard to tell that it's different from x86. It's not weird or different. Any linux user would feel just as much as home with Linux under z/VM as with x86.
Parent posted discussion of CPs and IFLs. Back when I was on the scene, there were also zIIPs and zAPPs. I think zIIP was for encryption or compression (maybe both). I believe zAPP was primarily for running Java workloads. It's been a long time, so my recollection may not be 100% accurate.
Probably the biggest shock to a newcomer of z/VM and z/OS is that terminal sessions are block-oriented (3270) and not character-oriented. With 3270 session, you type whatever you need to on a screen and then when a special attention key is pressed, your screen information is passed to the mainframe to process whatever you typed. No vi editing with 3270. Text editing on 3270 is with line-oriented editors like XEdit.
The scripting language for z/OS and z/VM is REXX. It's as high level as Python and is really a nice language once you get used to its quirks.
Here ends my mainframe brain dump. Can't guarantee that it's all correct or even still relevant, but hopefully gives a little bit of the feel for the environment.
[1] https://en.wikipedia.org/wiki/PR/SM