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).
A very common example of one NIC with multiple IP addresses is where the NIC provides a management interface in addition to what the OS sees. e.g. HP servers with ILO.