>>1
I think you had a pretty good handle on a definition in your OP.

The separation occurs between a [dead community] and a [dead website]. They are very different things. You can have an incredibly active website that has less of a community than Facebook. Or a very slow website like 4-ch that has a cohesive flavor and is used by pretty much the same people, or type of people, for decades. The relationships dividing them are simple mathematics.