A router passes packets by looking up the destination in its routing table of an incoming packet. If the destination does not exist the packet is dropped or sent out the default route depending on the configuration of the router. Routers work at layer 3 of the OSI model moveing packets based on the L3 address - ie. IP address, IPX address, etc.
A switch passes packets by looking up the MAC address of the destination in it's MAC table. If the MAC address does not exist in the table, it isflooded down all switch ports.
There are switches that do layer three routing. You create a VLAN that separates ports on the switch into different subnets, you assign an IP to the VLAN, then you route between the VLANS.
But a "layer 3" switchis a switch with a router inside. On these very same devices, they refer to either "routing" or "bridging" across ports.
It all depends on your configuration; but if all is working correctly, I would suspect that the noticable differential (ofconnecting your db server directly to the routing switch you have) would be neligable.