Once you admit this in a relationship do things change?

It definitely changes things. Most people are waiting for the other person to say that to ure them that they should go forward. It is very appropriate right before a birthday, Valentine's, or Christmas if the relationship is ready for it so that the other person will have a better idea of how to shop for gifts. It may not change a relationship much if the other person likes you but was caught by surprise. It will change the relationships with the few people who are not ready to consider the relationship and are scared you are acting too quick or if the other person does not want a relationship and that admission is the red flag they were waiting on to break the relationship. In the latter case, it would be beneficial to have that breakup as it was going to end up in a bigger heartache later when it would have inevitably ended anyway.