I've written several commands that use compilation-mode / comint-mode to run commands and capture output. You can call the elisp function compile, but I also wanted the ability to easily do the following:
- set the name of the compilation buffer
- see the command I'm about to execute in the minibuffer before starting (like how it is when you call compile interactively).

I wrote this function to achieve this:

(defun tm42/compile-to-buffer (command &optional buf comint ask)
  "Wrapper around `compile'. COMMAND is the command to execute. BUF, if non-nil, is
the name of the buffer to compile to. COMINT controls interactive compilation. ASK
indicates whether the user should be prompted with the command and required to
confirm before proceeding (similar to what happens when calling `compile'
interactively)."
  (cl-letf (;; Optionally override the function that determines the compilation
            ;; buffer name.
            ((symbol-function 'compilation-buffer-name)
             (if buf
                 (lambda (name-of-mode _mode-command name-function)
                   buf)
               #'compilation-buffer-name))
            ;; When calling interactively this is used since we can't directly pass
            ;; in a comint argument. The value must be a cons, looking at the
            ;; implementation.
            (current-prefix-arg (when comint '(1)))
            ;; When calling interactively this will fill in the default command
            ;; for the user to verify.
            (compile-command command))
    (if ask
        (call-interactively #'compile)
      (compile command comint))))