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.
Yes you can have more than one IP address when using a single Network Card.

Setting this up is different in each Operating System, but may involve creating a new Network Interface. This can look like a unique connection but will be using the same Network Card behind the scenes. OS X and Linux use this method.

To add a new IP address in Windows open up the network connection you wish to add another IP address to. Go to Properties –> Internet Protocol (TCP/IP) –> Advanced –> In IP settings, click add and add the new IP address and netmask.

This can be used to expose a server in two network ranges. For example one network range may be used for secure traffic which the other network range cannot access. Firewall rules could be different for each Network Interface.