Why is my IP different than my IPv4 adress?

[TechWizKid]

I thought the IPv4 address was the IP of the computer on the network? Does this mean that my IP changes once it goes through the router even though I don't have an active Proxy?

Render me confused.

Another question, why is it that some people frown upon Drive Images as a way of backing up the OS? I mean if the hard drive decides to crash, isn't the Drive Image the fastest and most reliable way to restore it to full working order? I mean it will have all the software needed for business functions and so forth.

Confused once more.