Basically an F-Clamp without the tail, extendable C-clamps can be quickly adjusted and provide more clamping power than similarly sized quick-clamps. Plus, since the bar doesn’t extend past the body of the clamp, you won’t snag stuff on it.
The top jaw of these clamps can be extended to fit the work piece and when it’s in place, you tighten the screw on the bottom jaw just like a C-clamp.
I could find two manufacturers of these extendable C-clamps — the first company is Stretta, which appears to have a website if you look at the clamp closely, but I can’t make it out or find it through other means. It also looks like retailers have cleared out their inventory of these clamps; one of the only places that still carries them is Woodworker’s Supply. On the gripping hand, the Grip version looks like it’s available in a few more places.
The 2″ to 3″ version and 3″ to 5″ version of the Stretta clamp can apply 300 lbs. of pressure and cost $8 and $11 respectively. The 4″ to 7″ and 5″ to 9″ versions can apply 400 lbs., but it doesn’t look like they’re available. The 4″ and the 8″ Grip clamps run about $8.