[dmbche]

At a glance : the internet is the scaffolding/structure, the Web is what people are doing in it.

The structure allows for great things. People suck. Hell is other people and all that.

[hunter2_]

I would qualify it ever so slightly:

The internet is the scaffolding/structure, the Web is what people are doing in a browser (i.e., over HTTP) in it.

Then there's also the stuff people do on the internet without a browser/HTTP. Nobody opens an IMAP/SSH/BitTorrent/IRC client or whatever and thinks of that as surfing the Web, because those aren't browsers nor are they primarily speaking HTTP.