I always think of dating as not that serious. For instance, some people are set up on "blind dates." People who are meeting for the first time. No one "blind sees" someone. So, to me, seeing someone is when the couple are more serious about each other.
. . . Of course, there's always the case of when one person is more serious than the other person is and tgey haven't really discussed it. The person less serious may say, I'm seeing someone. Whereas, the person more serious may say, "I have a boyfriend, (or girlfriend,)" to establish they think the relationship is more serious.