Diamond Systems were invented on 10 foot Carom (non-pocket billiards) tables as an aid to aiming. The diamonds are placed equidistant from each other and from the point of reflection on the cushion. This means that a corner has two diamonds one for the end rail and one for the side rail and neither diamond is in the center of the corner pocket (and neither is marked).
The diamonds are placed into the rails (3+11/16) such that a 3-rail shot from corner to corner will use the natural roll of the CB. The natural roll of the CB causes the CB to arc gently forward after each rail contact as the natural roll changes direction.
If you work out the "math" for this kind of physics problem, you will find that tables invariable "get shorter" as table size decreases. So on a 10 foot table corner to 3-rd diamond is square to the table and hits, on a 9 foot table, you need to go long by about 1/5 diamond (cloth and rail composition dependent), on an 8 foot table about 1/3 diamond. Tables with faster cloth will play more square than tables with slower cloth. Tables with dirty balls will play less square to the diamond system. Temperature and humidity also affect tables speeds and rail bounce patterns.
Diamonds are useful in lining up one rail kicks and banks, just remember the OB reflects 1/2 ball away from the rail. Here the marks are merely equidistant and used for helping you compute where to aim and then aim there.
Diamonds are NOT useful in lining up 2 rail kicks because the easy method is to place the tip of your cue at the point equidistant from the CB and the desired OB, then rotath the butt of the cue until it points directly at the center of the adjacent pocket. Translate this angle from the center to the CB and you have your direction for a 2-rail kick. (no diamonds needed) For these shots you MUST practice english control to make the system play true, mostly follow english with just a touch of running english is required--alternately you can shoot the CB true and compensate with slightly less angle towards the chosen reflection pocket. For extreme cases, one can shoot outside the given line and use "kill" english to get around other interfering balls.
As to snooker--I know nothing.