If you open any listing, the eBay item # is on the very far right, top line, under the description tab. It's very small, you have to look for it.
For years eBay displayed item numbers much more prominently. I don't know why they decided to make them so inconspicuous. Nonetheless they are distinct for the particular item, so if you give a customer that number and tell them to copy and paste it into the "Search" box at the top of any eBay page, the item will come up.
With a store you also have the advantage of a unique store name that you can give out to prospective customers. They can copy and paste the store name into the Search box just as for item numbers. Once they arrive at your store, they'll be able to access all your items displayed via the category list. You can also encourage them to add the store to their favourites in order to receive promotional emails from you, but personally I try to limit such emails to no more than once per month, otherwise people get fed up with the overload and will un-subscribe.
I think it depends on whether you're responding to an individual customer's specific request, or a general interest sort of inquiry. For the former, I'd give out the item #, for the latter my store name.
