Well, basically: Their tag wikis say the same, I see no other application for internet than for internet-connection and I don't see why we need to split the whole tag-system around connections into another one. And since I kinda lack the rep:
I'm not sure that's what's going on, though. Most of internet-connection questions seem to fit within the narrow scope of connectivity issues.
I recommend keeping internet-connection, at least for the time being. As for the connection tag, though, we should really get rid of that (by retagging its questions). There isn't anything practically similar about connecting to the Internet and connecting a USB mouse. The "connection" concept is too broad for a tag.