From what I've seen, "Social Justice Warrior" is a sardonic term and refers specifically to people who are over-the-top or trolling. An example:

Barbara doesn't understand the social construction of gender, and as a result inadvertently says some offensive things regarding transgender people. Lisa says "fuck you" and tells her that she's ignorant -- but will not tell her why, because in her words, "that's not my job." Kelly comes in, supplies a link, and says, "read this, Barbara. It might help you to understand." Barbara follows the link, and begins to research the issue. She comes back and apologizes for her earlier comments. Lisa says, "nice backtracking, you cis cunt. Check your privilege and get the fuck out of here."

Lisa is a Social Justice Warrior. Kelly is an activist.