Speaking of Software-Defined Networking, when it is said SDN switches or SDN routers, does it imply the "physical" routers and switches? If not, does it then imply that SDN controller emulates the routers inside its operating system including the routing tables too?
OpenFlow specifically - but also generally applicable to all of SDN - doesn't change anything about how your physical device forwards packets. The hardware is the same, and the pipeline that already existed on that device is unchanged.
What OpenFlow does is move the logic for programming the packet matches and actions from on the device itself (the local firmware), to a process that is running on a different device, which may have a view of more than one network element (and thus may be able to make better decisions with a better view of the world - or not). So, while you may configure network routing at a single controller, the controller is then distributing that information to a lot of devices to do what they have always done - match, modify, and forward packets.
you can't say it is emulated because emulating network element is running same physical device operating system and config over emulated hardware , it is totally software defined switch or router or firewall , for example Cisco nexus 1000V it is software defined switch , and it has many features like any physical switches and also has some specific properties like not running any type of Spanning tree protocol