From a user's point of view:
In this case, word pairs with the same meaning:
asynch/synch popup/exec non-modal/modalModal: when a thing ( dialog or in this case a menu) causes the GUI to enter a state where the user can do nothing else (other modes) in that app until the thing is finished.
With some variations: if the user clicks outside a modal menu, it is finished and returns a null result. Whereas in a modal dialog, the user must click in a Cancel button to finish the dialog, and can't click elsewhere in your app with any effect.
And even when an app is in a modal state, the user might be able to click in the windows of other apps (usually, it depends on the window manager, etc.)
From a programmer's point of view, your app event loop doesn't receive events when a modal dialog or menu is displayed. (Qt does receive and handle events, but doesn't dispatch them to your event loop.)