Difference between dating and being in a relationship
Although dating includes the possibility of romance or sexuality, people can be involved in a sexual relationship without dating and can date without ever becoming sexually involved.
People who are in relationships will walk around telling everyone about how they and their boyfriend/girlfriend are dating.
Dating and being in a relationship are the two most popular terms these days that have often been used again and again by several couples so much so that many would view the two as synonymous to each other.
Even though both of these involve two particular persons yet there is a difference between them.
If the person you have been seeing acknowledges that you are dating but doesn't want to use words like "girlfriend" or "boyfriend," she or he doesn't consider the relationship solid -- yet.
It is also possible that your partner simply doesn't like those particular terms, so you should ask.