A compliment is a polite expression of praise or admiration.
Flattering remarks, tributes, accoldaes, and praise all fall under the same umbrella.
If you get carried away as in a speech or eulogy the expression becomes an encomium which originates from the mid 16th century latin and is somewhat archaiac in these times.
I like to pass on a compliment or two along the way ...
Well, there's the kiss of death:
She's got a great personality !
There's the countryfied standout:
Gee, for a fat girl you sure don't sweat much !
And it's more urbane variant:
You look damn good to be as fat as you is !
You too can have ALL the je ne sais quoi P-Diddy thinks he has.
So I suppose the moral of the story is to be cautious in the rendering of compliments lest you mess up as I have witnessed in the hilarious past.