There are some odd exceptions (loopback, multicast, etc.) but in general, from a functional perspective, IP addresses fall into two categories:
1: Private IP addresses that are used behind firewalls, SOHO routers, etc that do NAT to get to the Internet. These generally start with 10.x.x.x, 172.16 - 172.31.x.x or 192.168.x.x.
2: Public IP's, that are fully routable on the Internet Generally all IP's that aren't private in the private range (with the exception of 127.x.x.x for loopback)
There are "classes" of public IP's, but those just define how big of a block is given out. A "Class C" is 255 IP's. A "Class B" is 65,000+, a "Class A" is just huge (16 million + IP's, 1/256th of all the Internet IP's available). In general, just ignore the "class" of your address. It means nothing to you or anyone else.
- G