He held his dog on a lead

or

He held his dog on a leash

Both of these are acceptable English sentences. The words 'lead' and 'leash' in this context are synonymous. But what's the difference between them? Some say there's no difference at all; others say it's a British/American difference; yet others say it's a dog-lover/'layman' difference. I hope the experts at ELU.SE can settle this issue once and for all!