I don't think the terms matter too much. I think (and others feel free to correct me if I'm wrong) that an open relationship typically is marked by more casual or short term outside relationships? As opposed to one or both of you developing a very serious other love. It sounds like you are worried that her other love is perhaps more serious that you may be comfortable with right now? And perhaps their NRE is difficult to deal with, making you feel insecure about the relationship. Now, who is this random person that told you two to break up? Is this some one who's opinion you trust and value? On what grounds do they say that? And why was your GF ignoring you? I guess it's hard to say much without more information.