There's no simple answer to the question, as it depends on context as well as where in the Spanish-speaking world you are. In an appropriate context, neither te quiero nor te amo is likely to be misunderstand as a way of expressing love. But there can be some subtle differences, as a discussion from our forum, which includes native speakers, indicates. Here are some excerpts:
Nootch76: What does te quiero mean? I was just wondering what this means when someone says this to another in the Mexican culture. Love, lust or what?
Garcilaso: Te quiero simply means "I love you." Of course it depends on the stress and the intonation, but to imply other connotations like in English I want you I think other verbs would be used, such as te deseo or the like.
There are sentences where te quiero won't mean "I love you," of course. Ahí te quiero ver, meaning something like "I'd like to see you there" in that context. Te quiero enviar una postal, "I want to send a postcard to you."
Encantame: Te quiero is appropriate for any love — spouse, friend, parents, siblings.
Te amo (verb amar) is usually reserved for your lover and not your friends or family, although I'm sure there are different countries/different ways. For gringos is best to stick to this pattern and we won't have to worry about doing it wrong.
ChrisAnvers: I always thought that this te amo was more usual in literature, no ?
Encantame: Well, it might be in literature, but it is also used in real life. It's not one of those things you don't hear except in a snooty book or poem. If you don't hear it much, and hear the other more, it's probably because you can say te quiero to a lot more people compared to te amo, so just the usage opportunity alone is going to be noticed, as you can say te quiero to anyone including your lover, but te amo is reserved for the intimate kind of love. So you just ain't going to hear it as often. It's definitely words for that special person. ... Speaking in generalities, again, customs may be different in some areas.
Lopezssn: Te quiero implies affection, love, care, not necessarily lustful. You can say te quiero to your mother, father , sibling, etc. It also depends on the region. It is similar to te amo.
Me gusta on the other hand when speaking about a romantic kind of like (not ice cream or candy) implies desire, lust, sexually appealing, sensually appealing. Me gusta ese chico, chica, muchacha, etc, muchacho, etc. Example: Sabes, me gustas mucho. You wouldn't hear that statement from one friend about the other.
... There are subtle intricacies that come with experience.
Araspace: Literally te quiero means "I want you," but how it is intended depends on the look in their eyes when they say it!
Aligoam: As many other have already explained, te quiero in Spanish, though meaning literally "I want you" translates as "I love you" and it is for family but also for love. We make no differences. I say te quiero to my daughter, but I also say te quiero to my husband.
Te amo, though it means literally "I love you," is more rarely used. I would say, only when you're feeling specially romantic.
I could translate "I want you" to Spanish in several ways, but I think the best one could be te quiero para mí or even quiero que seas mío-a. Of course, when using it to communicate sexual desire, you can also translate it as Te deseo.
Camicat: Language must always be interpreted according to context i.e according to the conversation. ...
Jazzeerun: Te quiero or Te amo literally means "I love you." You may also say te estraño, I miss you.
Ibaquerena: Te quiero can be both for people close to you or for friends. It all depends on the importance you give to the words. You can tell a good friend te quiero and it may just mean the "I love you" that some friends tell one another without any romantic connotation. On the other hand, you an tell your wife te quiero mucho and it may mean "I love you" in the sense a lover would use it. Te amo is mostly used among people who are learning Spanish from a textbook or in telenovelas.