Which ones you can use are determined by the video driver you have selected in settings > drivers.
The default video driver is “gl”, which can use GLSL or Cg (the mupen64plus core doesn’t always play nicely with Cg shaders, but everything else should be fine). The d3d driver can only use Cg (some cores don’t work with the d3d driver). The vulkan driver can only use slang (a couple of cores don’t work with vulkan).
Confusing, I know. Basically, the GLSL ones are the most safe/compatible. Cg used to be the main one we used but Nvidia deprecated the language, so we’ve started moving away from them. Slang/vulkan is new and powerful but not all GPUs/cores support it.