The £80 is to transfer the plate directly to another vehicle, whether it's owned by him or you. It's all done in one transaction.
If it's put on retention, (I think it's £100) the plate is removed from the donor car which gets its old plate back usually. When the seller gets the certificate back from DVLA, it's then passed to you to send away to DVLA in order to assign it to your own vehicle.
In my experience, each stage takes a couple of weeks.