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

Answer: 
Yes, you can have multiple; they are not one to one.

A single network card can do this in a couple of ways; it can answer for multiple IP addresses with a single MAC address (assigning multiple addresses to a NIC in most operating systems will do this), or with multiple MAC addresses (virtualization platforms behave in this way).
Not only is this possible, it is very common. A network card may have multiple IP addresses. This is a concept called [multihoming](http://en.wikipedia.org/wiki/Multihoming). There are other variants of multihoming as well.