If we are talking about wigs....
A U part wig is attached and the middle of your hair is left out, you will need to either perm, press or use a closure to blend your hair with the wig.
A quick wig is a wig with a long comb in the front and back of the wig, where you would like out the entire front of your hair from ear to ear and you would blend with the wig.
While a quick weave is a weave that is bonded down and covers all your hair so none of your hair is out at all, but it looks more fake then the quick wig or u part.
At least this is my understanding....hope this helps.