Routes manage the path of a customer's outbound calls, while DIDs bring inbound traffic to the customer. They both take care of the transit of a SIP audio call from caller to callee, and have many of the same challenges to their quality in common.
The technical barrier for providing termination services (routes to PSTN) and origination services (DIDs that get calls from PSTN) is so low that in countries and regions where VoIP is under monopoly, or where a cartel of big companies control the market imposing hefty prices, the business opportunity is so compelling that a plethora of independent operators, of widely differing reliability and regulation compliance (or which are outright illegal) discreetly populate the scene.
Talking about routes and DIDs to and from these destinations, it is often referred to by the term "grey" market. That's because one side (you, the end customer) is white in the open, regulation abiding, while the other end is black in...