A pop-up is a modal view that can either take form as a pop-up menu or a pop-up dialog. To my understanding, when we use the word “pop-up”, what we want to express is the pop-up motion effect on the call-out of the UI treatment.

A dialog is a type of modal window that appears in front of app content to provide critical information or ask for a decision

The term "modal" is sometimes used to mean "dialog", but this is a misnomer. A modal window describes parts of a UI. An element is considered modal if it blocks interaction with the rest of the application.