"connection" refers to the underlying transport services
used to carry the protocol exchange, as well as
associations established by these services.
Sorry to continue teasing at this as I know we want to close on it, but
let me suggest "transport connection" rather than just "connection". I
think this would be more consistent with the use of that phrase in the TLS
spec. And it would make all the terms two words (or two strings, at
least).