add_action for admin_init hook with a parameter

What you want is quite possible, but not exactly mainstream technique. Take a look at my Implementing advanced add_* function wrappers question.

However your real issue here is not being unable to pass arguments. It is lack of context.

1. The simplest way to track context is inside your hooked function (check what page you are at, do something accordingly).
2. Slightly more complex is adding your own dynamic hook (Post Status Transirions are great example).
3. Even more complex is contextual hook.