Although it looks like Mosely, it is the Mossley Inn. The address would work out to be 109 Armitage, and if you look further down that census page, you will see the addresses change from Armitage to Mossley.
In the 1901 census, the inn was owned/run by George Clements, Inn Keeper and Pub, 109 Armitage Rd, Mossley Inn (written much more clearly).
As a side note, the son-in-law Frank Critchley is listed in an 1895 article entitled "Receiving Orders". I don't know if that means his business went into receivership, or what. At that time, he was "trading" as Critchley & Willis. The article lists some of his prior addresses (and mentions a Henry Willis), but nothing about the Inn, or Armitage. If Frank is important to your tree, I can expand on the addresses given.
This doesn't answer your question as to what the definition of "inn" was back then, but it looks like at least part of it was a pub!
Google is showing a Mossley Tavern at 95 Armitage.... not sure if the road was renumbered or not, so it could be the Mossley Inn vanished, and a new pub appeared.