For Air France Hop and Lufthansa Regional, one important detail is that they all originated in acquisitions, mergers, or agreements with smaller independent local airlines serving one specific region of the country (don't know anything about Air Canada / Jazz). Even after being integrated in the network of the parent airlines, keeping them separate in terms of branding and operations can have some advantages, including different contracts and pay scales for the staff.
Such flights did not seem "regional" to me at all, as we crossed a major distance in the country.
They are still regional in the sense that these airlines don't operate international and especially intercontinental flights, unlike Air France and Lufthansa. You could interpret that as staying in the same region of the world or serving other regions of what are ultimately rather small countries but no matter the terminology the difference is quite clear.