Most basic.. there is an aluminum piece machined to have a wedge in the bottom same as the stem you have, (7/8" or 1")

But, it's machined to be round and the top is the 1.125" so you just fit the threadless stem of your choice there.

the BHP 20 in 1st link, is for a 22.2mm (7/8") quill stems , the fork OD is 1" (1" headset 32mm wrench)

the BHP 21 is for an oversize threaded headset and as a stem riser* for threadless steerers .
(* I have one used for that)

and threaded forks with a 1" ID, and a 9/8" OD headset adjustment uses a 36mm wrench..