Hi Tim.
As I see it a Coin Assembly is the proper term for an effect where a number of coins, placed seperately, gather in one place - usually a corner of the table/mat. Matrix is the name Al Schneider gave to his own version of the coin assembly plot.
As an example of what I mean take the Ace Assembly routines that we all do. One of the most popular over recent years is Bob Kohlers Aces in their Faces, this is Bobs own version of the Ace Assembly. If I come up with a routine that is nothing like Bobs either in effect or method, but the aces still gather in one pile, could I call it Aces in their Faces ? I would say no. Unless I am using Bobs routine, or something that very closely resembles it, then it is not Aces in their Faces.
By the same token Als Coin Matrix uses 4 cards and 4 coins for a coin assembly. If someone is not using 4 coins AND 4 cards then it is not Als routine, and therefor not Matrix. Chink a Chink and Matrix are 2 completely different effects. A bare handed coin assembly is essentially Chink a Chink using coins, and Chink a Chink is certainly not a Matrix.
Matrix is a term that seems to have stuck (wrongly) to mean almost any coin assembly routine. Just as an ace assembly is not Aces in their Faces unless you are doing Bobs routine, a coin assembly is not Matrix unless you are doing Als routine. So the difference between a Matrix and a Coin Assembly is simply in what you do. If you are doing Als routine or something which very closely resembles it then you are performing Matrix, if not then you are performing a coin assembly