Okay, I'm a bit baffled by this because I've never noticed it before and I've installed Jetpack on a few different sites now. So I don't know if it's an error or a glitch or actually supposed to be this way or what.
So, I know Jetpack has to connect to WordPress.com - on my personal site I see it's happily connected, for instance.
Yesterday I installed Jetpack for another site and linked it to the appropriate WP.com account. And then saw an error that it wasn't connected and so did as prompted. Now on the Jetpack page I see "Connected to WordPress.com" AND "User linked to WordPress.com" in the banner. And I'm totally stumped as to why. Oh, and if I unlink either of them, Jetpack doesn't work and gives me the naggy error thing to connect stuff.
I don't see it on any other site I have access to using Jetpack, whether I'm currently logged into WP.com or not. I just see "Connected to WordPress.com."