Casual Compile is a user interface for the output of the compile command ((emacs)Compilation). The output buffer’s major mode is compilation-mode whose commands are surfaced by Casual Compile.
In similar fashion, output of Emacs-wrapped Grep commands ((emacs)Grep Searching) is also supported by Casual Compile. This is because the output of Grep commands use the major mode grep-mode which is derived from compilation-mode.
The screenshot below shows the menu for compilation results.
The screenshot below shows the menu for Grep results. Note the menu label changes based on the output mode (in this case grep-mode).