Your other question is more difficult
I use the definition 'prototype' where one or only a couple only are made, and they are in some way distinguishable from the issued article, if indeed they were issued. Also, in some cases, it will be to test a new production method/make a new product.

A 'sample' is what it says - a sample of what can already be done/has been done. Notched samples, for example, are produced at the same time as the actual chips are produced.

Neither are necessarily made for the casino or with the casinos input but both could be
BTW - I reckon the Luxor chips were made for the casino even though they were samples. I would not call them prototypes as way more than a couple were made.

I would not regard samples that exist with manufactures logos on the back for example as falling into either of those categories though.