You're referring, I think, to the doctrine of the "Dormant Commerce Clause," (the "DCC") also known as the "Negative Commerce Clause."  It's taught in law school through Gibbons v Ogden, where the doctrine was first enunciated in the 19th Century.  Generally, the doctrine is that, since Congress  *could* pass a law regulating some particular instance of interstate commerce, that states *can't* pass such a law.

The DCC is typically applied when a state tries to tax or regulate something in a discriminatory or protectionist manner that might lead to the balkanization of the states.  For example, a state law that prohibits the export of shrimp unless the shrimp are first processed in that state would be held unconstitutional under the DCC.  The law clearly seeks to protect in-state businesses at the cost of out-of-state businesses.

There is a well-established exception to the DCC: where a law seeks to protect the public health or safety of the citizens of the state.  State money transmission laws clearly seek to protect the state's citizens from the harm of undercapitalized or fly-by-night money transmitters.  Money transmission laws fall under this exception.  It might also be the case that there is a federal statute out there that explicitly authorizes these laws, in which case they would fall under the "congressional authorization" exception as well.