Perhaps this might answer your question. I believe the term "Drop Chip" mostly has applicability to playing poker and it represents the "rake" amount the house gets for each hand dealt. Not all houses do this, but some will use a specifically denominated chip (say a $3 or $4 chip) and from every pot will pull the rake amount. If the game is $2 - $4 and only $1 chips are used, then the dealer has to pull 3 or 4 $1 chips from each pot and "drop" them into to Drop Box. At a busy table or house, the Drop Box will fill very fast and then it has to be emptied more often which causes additional costs (labor).

But if the house provides the dealer with a tray "drop" chips and the dealer pulls the $1's from the pot, putting them into his/her tray, grabs a "drop" chip and puts it into the Drop Box, then it does not fill-up as fast. However, the dealer's tray might fill up with $1's, but he/she can use them table buy-ins or when they rotate, they can stop by the poker room cage and exchange them for more "drop" chips.

Some house do not allow the "drop" chip to be used for anything other than being a "drop" chip, while some houses will. The Tropicana did not allow their poker room $4 chip to be used for anything other than a "drop" chip. The same with the Stratosphere, and those chips are harder to come by and usually demand more to acquire.

The Orleans has a $2 "drop" chip, but they also allow it to be used in regular poker games like $2 - $4, but many players just use the $1's as they allow for bigger stacks with less money!

I hope this helps!

Jim