Mac OS is a popular family of operating systems. It was one of the first systems to Pioneer the Graphical User Interface.
The "classic" Mac OS is characterised by its lack of the command line, and encompasses the different Mac OS' from 1984 to 2001. It lacks primitive multitasking and protected memory and is composed largely on 68k assembly code.
OS X (re-branded from "Mac OS X" in 2012) is the latest version of the Mac OS operating system (initially released in 2001), and is also the basis for iOS. It is instead based on NeXTSTEP and UNIX.
Wine is one of the easiest and most popular way for Linux users to run programs written for Microsoft Windows. The Wine team has created a port for OS X that is well maintained and in a usable state.
Boot Camp is an official piece of software included with OS X that assists users in installing and running Microsoft Windows in a partition on the hard drive. The most recent version only includes support for Windows 7 and Windows 8.
The Unix Shell "bash" available on OS X is a very useful tool for doing system tasks. If you use OS X as your main operating system, then it is heavily recommended that you learn how to use it.
Google Code University provides a good starting guide.