Difference vector target and genomic target
Genomic DNA is a DNA that has whole set of genetic data of an organism. You usually extract it with a whole DNA extraction kit.

Vector DNA is a vector (usually a plasmid, it can also be artificial chromosome,...the type of vector depends on the species and strategy you are using) that has you desired string of DNA in it (for example a gene you want to insert in to a organism) and you are using it to get your recombinant DNA to the organism.

I hope it helps!