GIVE ANSWERS - Español

" Te Amo" is used when you want to have a loving relationship with another person and " Te Quiero" can be used to express a certain kind of liking

"Te amo" is used when you feel something very strong and special for someone. You can say, for example, to the person with whom you have a relationship, but not at the beginning of it, another person may not feel the same
On the other hand, "Te quiero" is not so strong and you can say it, for example, to your family.

As Sujeily said, you say “te amo” only to people for whom you feel a strong feeling, like your couple (with time and only if you feel it), maybe your children, your parents or siblings usually, on the other hand, you use “te quiero” for example at the beginning of your relationship with your couple, to your friends (if you really care about them) or your family. In the past it was not common to say “te amo” even to a close friend, instead they could say “te quiero mucho”(I love you so much), but things are changing a little nowdays, so these days you may hear a few cases of close friends saying it without being a couple. A funny fact is that when you do some important favor to another person, some people get so happy that they can tell you "te amo", it's like telling you that no one else would do that favor and, as you did it, you are amazing, it does not matter that both of you are from the same gender.