Just to clear up a misconception, Apple and Microsoft are not operating systems. They are companies. Windows and Mac OS are the operating systems.
IBM is mainly a hardware company but they used to develop an operating system in partnership with Microsoft known as OS/2 (In the 90's).
The biggest contenders on the PC operating system market (Although some would argue a Mac is not a PC :/) are Windows, Linux and Mac OS.
Mac OS is generally used for Apple's own computers (iMac and Macbook), it also costs money.
Windows is another operating system that costs money, it is the most widely used OS by consumers.
Linux is a FREE operating system. Everyone has access to the source code, and unlike the former two, can be modified and redistributed without charge. It usually takes a more tech-savvy person to run Linux but new distributions such as Ubuntu are much more user friendly.
I hope that clears things up let me know if you need more clarification.
EDIT: Yes, Ubuntu is a particular distribution of Linux (There are bloody loads of them). And you are correct, Linux is the free, open source version of Unix.