You do sort-of have a "normal file directory", except the file names use "." to separate parts where the systems we're used to use "/" or "\". And the concept of a directory (without any files in it) does not exist. Imagine everything in your company is in one big S3 bucket. In fact, a lot of mainframe concepts that seem alien make more sense when you compare them to cloud services than PC architecture.

Much of the tooling was built around the concept of punch cards, with 80 columns per line. This is fairly obvious in COBOL where certain columns have special meanings. The various visual editors on the system were built with this in mind; the one I used most was a sort of "what if vi, but you enter commands in the sidebar instead of prefixing them with ESC".

You can't (or shouldn't) run any programs directly by invoking the executable; you write a JCL job. Their main purpose is to ensure that everything gets billed correctly and doesn't interfere with production. They are sort-of like shell scripts, but more clumsy and way more powerful. For example, in a unix shell you often use 3 file descriptors that almost every program has (input, output, error); in JCL you can define as many as you want and map them to files, and this leads to another oddity, which is that in your programs you don't access files directly, just the streams that you define in your JCL. They have a block where you can declare things like "this job is low priority and can run after office hours and should take no more than 30 minutes, bill the CPU time to the IT department, project 12345".

The programming model has various ways of accessing files; most of the time you don't use them as streams (like you do in unix), but define their record layout. They are expected to map directly to the in-memory layout of your COBOL data structures.

...which are also weird: The data types are not what you expect, at all. Strings are often not ASCII or UTF-8 but in a completely different encoding from the dark ages of computing. You don't think about this until you exchange files with a programmer in the modern world and all they see is garbage. There is a decimal floating point data type that internally stores 2 decimal digits in each byte, which some of the available CPUs can work with natively.

There are hierarchical databases that feel distantly-related to some modern nosql databases (but without there being any direct links between them).

IBM's DB2 supports all of these oddities with various extensions that you won't see in any other SQL database implementation. But that is genuinely the easiest way to deal with all of this.

I'm sure there is way more but it's been more than 20 years...