I'm a programmer, in the industry these days everyone uses "Software Engineer" for job title/resume purposes, or "Programmer" in parlance because it sounds less snooty.
Software Developer is the same but nobody uses it. Some government jobs and government contractors continue to use the title.
People with the Application Developer title generally wouldn't be programmers. They are probably trained on a workflow using a particular application, which may involve scripting or light programming. I.e. they can configure interfaces on a middleware application.