Question: Are network cards and IP addresses a one-one map?

Answer: 
A single physical network card definitely *can* have multiple IP addresses. This is almost essential when implementing server virtualization: with multiple virtual servers running on the same physical hardware, each needs its own IP address.
IP layer (the ip address) is completely independent from the physical layer (your network adapter). If your operating system has properly implemented the OSI stack or some close model of it you should be able to easily define several incoming IP addresses on a single network interface. Handling incoming traffic over multiple IP's is pretty easy within linux. However, it's a little more tricky making outgoing traffic have different source IPs when sharing a single interface. Applications typically default to use the primary IP for outgoing source if you don't do anything special to force another IP to show up, but it's definitely possible to do this as well.