So, the thing is--in theory, we could make up whatever tag we want. In practice, you wanna go with things that apps and the community at large has agreed on. The first wiki page I linked has the most common ones, which you generally want to go with if you can...but when you can't, there are plenty of others.

This page lists all of the shop tags documented in the wiki, there are a few hundred: https://wiki.openstreetmap.org/wiki/Category:Tag_descriptions_for_group_%22shops%22

There used to be a longer explanation here, but it's a moot point...reading the osm wiki's description of how shop=deli should be used and searching the local area to see other examples, I think it's actually a pretty good match. It looks like a bunch of Montreal shops with that tag are specialty food stores like this one (though not all italian of course)