A routing switch is a specialized type of switch that also performs many of the tasks of a router.
Routing switches are very similar to a typical router and in many cases they also inspect the incoming/outgoing network traffic, support of all major routing protocols and most of the routing of data/traffic to the next hop/router. However, routing switches also include switching abilities, and can forward data according to a device's physical address. The main difference between a routing switch and a router is in their hardware structure, as the routing switch incorporates the functionality of both a switch and router but uses hardware routing, whereas typical routers use software routing.
A routing switch may also be known as a Layer 3 switch.
Techopedia explains Routing Switch
Routing switches are an innovative amalgam of two core networking devices, allowing them to achieve greater capability and performance. A routing switch can perform nearly all the same operations as a router and switch by transmitting data on LAN using Layer 2 switching techniques, and over distant LAN by integrating Layer 3 routing operative methods.
Routing switches were introduced into the market to improve the network traffic optimization in organizational wide LAN, which spread over many nodes and smaller LANs. The Layer 2 switches didn't provide the required efficiency in transferring data over largely dispersed LAN; therefore, Layer 3 switches not only manage the traffic within a single LAN segment, but they also provide optimal performance in managing and transporting data over distant corners of the LAN. Routing switches' hardware-powered routing capabilities provide for faster and better performance in a variety of scenarios. Routing switches can also be a cost-effective alternative to routers.