A disease vector is an insect, animal or other organism which spreads disease indirectly. It is not the the thing which causes the disease, but is a "carrier". Mosquitoes carry a parasite which causes malaria. Dogs can carry a germ which cause rabies.
In genetics, a vector is an agent, such as a virus or a small piece of DNA called a plasmid, that carries a modified or foreign gene. When used in gene therapy, a vector delivers the desired gene to a target cell.