'Puppy love' is usually something you go through in your teens-early 20's, when you've never been in a serious relationship before and have nothing to compare it to. Important parts of the 'relationship' are usually missing or ignored, such as proper communication, a thorough understanding of each other as people, and the ability to have a life separate from the other person because 'you just can't stand to be without them'. You don't usually recognize it until you get older, have an adult relationship, and then look back and realize it for what it was.

True love is love without needs or wants or conditions. You don't love someone 'if', you love them 'because'. You understand that you as people are not perfect and neither is your relationship. You accept them 100% for who they are. You would give your life for that person without a second thought. And like Donut said, there is no lust, control, or jealousy.