Is NAT the same as a Routing with DHCP in the virtual VMnet 8 (NAT) in VMWare? Or how does the routing take place in these virtual environments?
How a host gets an IP address is unrelated to how traffic from it is subsequently NATed and routed or just routed. That is decided by the configuration of the gateway/router it uses to communicate with another host/network.
This is a potentially dangerous misunderstanding, not sure how you came to have it. Perhaps you should try asking a broader question about what your trying to achieve.
Also read the wikipedia article on NAT.
First you should differentiate Routing and Forwarding.
Routing determines the packages complete way through the network.
The process of Forwarding instead decribes the decisions taken by a single node to communicate to the next neighbor.
NAT (Network Address Translation) describes methods to used to replace the adressinformation transmitted in a packet.