Forging, as can be seen from the definition of wiki, focuses on "using local compressive force" and using local force. Then punching and shearing involved in forming should belong to forging, but stretching belongs to forging. I'm still investigating. For English majors, I have to look at stress patterns. . . I hope to discuss the progress with you in depth.
Cold upsetting is a forging method of upsetting (usually local upsetting) metal bars. Cold heading is usually used to manufacture the heads of screws, bolts, rivets, etc. This should be included in forging.
To sum up, it should be cold forming & gt cold forging & gt cold upsetting.