Are the handcuffs that are used for prisoner transfer (the belt around the waist, hand cuffs and ankle cuffs) universal also?
Handcuffs and their keys are not universal, despite similar appearances of what many consider a "standard" cuff and key configuration. Manufacturers have different specifications and tolerances for their specific products. Admittedly, many are so similar that some keys will open other brands of cuffs - but certainly not all.
Nor are the locks/keys always similar. In the mid-'70s through the late-'80s Smith & Wesson manufactured an entire series of handcuffs with round "barrel-style" locks/keys coded "A" through "G" inclusive. One needed a "D" key to open a set of "D" cuffs. These types of restraints were very popular with US federal agencies at the time. By 2000 these "barrel" lock cuffs had largely been supplanted by the more common "standard" cuff/key configuration (such as characterized by the Peerless product line
http://www.peerless.net/). FWIW, I suspect that cost and convenience were among the mitigating factors in the gradual transition. From an operational standpoint, it could be a hassle to have to have a dozen or so different keys readily available.
Many manufacturers still make more secure locking mechanisms.
Leg irons are slightly larger in all respects, and the respective keys are typically more robust. A cuff key, while very similar in appearance, might work, but more often it won't.
Waist chains may be of an average length to span the girth of most people, but the end link must be large enough for an opened cuff to slip through, yet narrow enough to fit through another link when the chain is snugged around the inmate. Once secured on the wrists, cuffs won't fit through the large end, of course. The other end of the chain may have a simple clip to attach to a link mid-length, usually in the middle of the prisoner's back. Or, it may have a padlock so that the dangling length may be secured to the links of the leg irons.
Then there is the "black box" - a hard plastic polymer (or steel) box (roughly 4"x3"x1") that closes around the handcuffs & secured waist chain loop, and blocks access to the locks on the cuffs. the black box is secured with another padlock.
Handcuffs of any variety are at best only temporary restraints. Seasoned cops know to always double lock their cuffs; that prevents shimming/slipping the claw. Double locking is what the little protruding pin on the other end of the "standard" key is for. To open a double-locked set of cuffs, one must rotate the key typically 180* in both directions.
I hope you find this helpful.