There is a noun, "dialogue", which is in common usage and means for two or more people to converse.
There is an adjective, "dialog", which is technical jargon and denotes that an element of a program or application requires user input to complete a task. It is almost never applied to anything except "dialog box", although I have heard certain (heretical) people talk about "dialog menus" in the early 1990s.
There is an intransitive verb, "to dialogue", which is in use among business professionals as a way to identify discussion that involves a commitment. If you "talk" about something, no result is necessarily intended or expected; if you "dialogue" about it, the discussion is expected to stay focused on the topic and reach some productive result.
The word "dialogue" may be spelled "dialog", but the word "dialog" is never spelled "dialogue". There is no such thing as a "dialogue box", unless you're jocularly referring to a chat window.