what is the relationship between a restriction enzyme and a sticky end?

Answer 1

Restriction enzymes cut DNA with either blunt ends or sticky ends. Blunt cuts leave the two strands the same length. Sticky ends leave one strand longer than the other. This produces either a 3' or a 5' over hang depending on which strand was cut shortest.

Answer 2

Restriction enzymes cut DNA. But many of them don't cut straight through. One strand overhangs the other, so there are unpaired nucleotides that can stick to other unpaired nucleotides. Hence, "sticky end."