A global hotkey is a chord such as Option-Space, Control-Alt-Space, or a modifier like fn, bound at the system level. The OS delivers that event to the dictation app even when a different process owns the cursor. That is what makes press-and-speak feel like a system feature. Conflicts happen when two apps claim the same chord, or when a game swallows keys. Good software lets you record a new binding and test that the event actually arrives.
Permissions are the unglamorous half of the story. Seeing keys globally may need Input Monitoring or an equivalent accessibility grant. Typing the result into another app is a separate grant: the hotkey starts capture, then text injection pastes or synthesizes keystrokes into the focused field. Denying one permission can yield a silent failure — you hold the key, nothing happens — which looks like a broken hotkey when it is actually a privacy prompt you dismissed.