OCaml and Go are not considered systems programming languages, in part due to having required heavy runtimes and garbage collection.
So they're scripting languages?
Scripting languages would be (usually interpreted) languages for doing small snippets of code. Examples would be bash, Applescript, python, etc.
Application languages are generally managed/GC'd languages with JITs or AOT compilation for doing higher-performance apps. Examples would be Java, Go, Ocaml, Haskell, etc.
System languages are generally concerned with portability, manual memory layout, and direct hardware access as opposed to managed APIs. Examples would be C/C++, Rust, Zig, Pascal, etc.
Traditionally,
Scripts are programs that carry out a specific task and then exit. If failure occurs, it is usually on the operator to fix the issue and run the script again. I agree that bash, AppleScript, Python, etc. are geared towards these types of programs.
Applications are programs with interfaces (not necessary graphical, but can be) that are used interactively. If failure occurs, the software usually works with the user to address the problem. It's not completely unheard of to use Go here, but I wouldn't call that its strength.
Systems are "forever"-running programs to provide foundational services other programs. If failure occurs, the software usually does its best to recover automatically. This is what Go was designed for – specifically in the area of server development. There are systems, like kernels, that Go wouldn't be well suited for, but the server niche was always explicit.
Your pet definitions are fine too – it is a perfectly valid take – but know that's not what anyone else is talking about.