In Spanish to say "I love you", we say both "te quiero" and "te amo", but we use them according to the level of our feelings.
Both phrases are used to express the love that you have for the other person but “te amo” is a very special phrase. You cannot say “te amo” to everybody. It's only used when you have a deep feeling for someone, and it is not recommended to say "te amo" to your significant other at the beginning of a relationship because you must be sure about your feelings.
Also, you can use both phrases when you want to express love to your family.