here where I live and work the word "committed" used with the word "relationship" means you and the partner are together with each other and no one else.

here where I live and work the word "open relationship" means you or your partner can date/ have sex with / what ever with other people.

My wife and I were in a "committed relationship" meaning we are bound to each other and only each other, for many yrs. we lived together in a committed relationship until last yr when our state (New York) passed the gay marriage law, at which time my partner and I married. we are now not only in a "committed relationship" we are married to each other and only each other in sickness and health for richer or poorer, unto only each other 'til death do us part.

my wife is a fantastic woman who before we were married accepted all of me not just the aware part of me but every one of my alters too. We both knew we had found our "life partner" about 6 months into the relationship so we moved from our "open relationship" of dating on and off to a "committed relationship"

when you find that one that you are "committed" to you wont even think about having an "open relationship" of dating and having sex with others, because everything you could possibly want and need is right there already at your side, already in your bed, already an extension of yourself type feeling.