Vertical gene transfer uses reproduction as a means of gene transfer through generations, whereas horizontal gene transfer uses non-reproductive methods of gene transfer.

gene transfer in eukaryotes

Gene transfer in eukaryotes may come in the form of mitosis or meiosis. However, horizontal gene transfer, to my knowledge, does not occur in euks.

Horizontal gene transfer is when a cell's DNA is transferred to an individual without reproduction. Bacteria have the ability to accept plasmids from other bacteria, and then incorporate the DNA in to their own genome.

Horizontal Gene Transfer is probably the term you are looking for

Get bitten by a radioactive spider. There is a possibility of horizontal gene transfer.

A xenologue (also xenolog) is a gene sequence in which similar sequences can be found in different species, due to horizontal gene transfer.