Mac OS is a popular family of operating systems. It was one of the first systems to Pioneer the Graphical User Interface. It is also one of few platforms to have survived a move to a new processor architecture. It actually survived two; once from Motorola's 68k to IBM's PowerPC, and again to intel.
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.
Unfortunately due to its age, in order to run apps from the old "Classic" System you need an emulator. You can effectively think of the following as the Macintosh equivalent to DOSBox. Three option are available: Sheep Shaver, Basilisk, and Mini vMac. To categorize them in the simplest way possible, Mini vMac is for black and white 16/24-bit 68000 based Macs, Basilisk is for color 32-bit (020, 030 & 040) 68k Macs, Sheep Shaver is for classic PowerPC Macs.
macOS (re-branded from "Mac OS X" in 2012 to "OS X", and then 2016 to its present name) is the latest version of the Mac OS operating system (initially released on March 23, 2001), and is also the basis for iOS, as well as its other siblings in Apple's product lineup. It is instead based on NeXTSTEP (which in itself is derived from 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.
Mouse Acceleration Preference Pane allows you to adjust, or disable, mouse acceleration in macOS; something that's not normally tweakable.
Additionally macOS once had a bug that induced mouse lag, going as far back as 10.4 (Tiger). For the longest time the solution was to remove or disable Apple's AppleUpstreamUserClient.kext via the terminal  , i.e.
cd /System/Library/Extensions/ && sudo mv AppleUpstreamUserClient.kext AppleUpstreamUserClient.kext.old
A slightly more solid fix is available in the form of SmoothMouse. Note that it requires 10.8 (Mt. Lion) or later to function, though some earlier betas for 10.6 were available. OS X 10.12 (Sierra) and later do not have mouse lag issues.
Similar programs existed for the Classic Mac OS as well.
Boot Camp is an official piece of software included with macOS 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 10, though earlier releases supported XP through 8.1.
The Unix shells "bash" and "zsh" (the former being the default on every release until 10.14 ("Mojave"), the latter being the default since 10.15 ("Catalina"); though both are available as options) available on macOS are very useful tools for doing system tasks. If you use macOS as your main operating system, then it is highly recommended that you learn how to use them.
Google Code University provides a good starting guide.
Rosetta is a software emulator for Intel Macs that enables them to run older (OS X native) PowerPC apps. This can be useful for running games that didn't receive a Universal Binary update post-2006, such as the Mac OS X release of Fallout.
Similar to Microsoft's NTVDM for DOS apps, the classic environment was a compatibility layer for OS X that allowed it to run classic apps at roughly native speeds. Note that the Classic environment is NOT an emulator, and as the classic OS is based entirely on PowerPC (and/or 68k) code, it does not function on Intel Macs.