I need to know the difference.
What is the difference between te amo and te ame?
Te amé doesn't sound right. I don't think you would love someone as a one time event, so the preterite isn't likely. Te ame is the subjunctive. That might fit in a subjunctive clause somewhere and is probably more likely than the preterite.
te amo = I love you te amé = I used to love you (I loved you)
'Te ame' is the subjunctive form but I doubt that someone would use it that way without you being able to understand what they mean. I would assume it's the 'amé' version you meant.