The ones I'm actively running at present (Cold War Pulp, and the Occult WWII in India campaign) are intermediate. The characters are free to do what they like, within the in-game constraints of the organisations that employ them and send them on missions. Those constraints are pretty loose, because the characters have a lot of discretion about how they do their missions.
One character in the India game absented himself from a scenario (and probably much of a second one), because the royal family of Afghanistan invited him to go on Hajj to Mecca with some of them. The organisation was perfectly willing to allow that; having more political contacts with Afghanistan is good, and since the character's powers are tied to his Islamic devotion, he's liable to improve them by a pilgrimage.
This kind of "mission framework" is theoretically contiguous, but mostly episodic in practice.
The Avalon AD&D1e campaign is contiguous. We had a few months of downtime recently, but that was because one of the characters wanted to do some magical study, and everyone else could find worthwhile uses for the time outside adventuring, mostly working for their various churches.