Ok, first some terminology. The typical type of clamp used on a mill, and the type I think you're calling a bar clamp, is called a step clamp and looks like this...
https://www.mcmaster.com/step-clamps
Bar clamps look like this...
https://www.mcmaster.com/bar-clamps
and are more often associated with woodworking applications.
The clamp detailed by backyard_cnc has a significant advantage over the typical step clamp used with a staircase block. It doesn't need the staircase so it's easier to set up (no third hand required) and can clamp over a significant height range without need to move to a new step on the staircase. When a height block is required, a simple flat block can be used - much less chance of the clamp slipping off the block.
I'm not sure of the correct name for clamps of this type. Bessey makes them and I've heard them called "Bessey clamps" but a more frequently heard name is "hold down".

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