Browsing depends on the creation of a Master Browser list. The creation of this list requires that the PCs be in the same network subnet, as it depends on Broadcast to the subnet broadcast address.
Your second IP is either in a different subnet because the network portion of the address is different; e.g. 10.0.x.x while the first is 192.168.x.x; or because of the subnet mask used.
You would have to use an LMHOSTS file, or have an active WINS server to resolve honstnames if you intend to use different subnets.