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.
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.