[lili5689]

I don't understand the discrepancy between the words Apple and Mac, or between the words Microsoft and PC. Are Apple and Microsoft the names of the operating systems?

Are Macintosh and PC the names of the actual hardware of the computer? Does Microsoft actually make the hardware, or do separate companies? Are those made by separate companies still called PC?

[Headrush]

There are differences between the exact meanings and the generally accepted meanings of several of those words.

Apple and Microsoft are companies.
Apple develops an operating system called OS X.
Microsoft develops an operating system called Windows.

Apple develops hardware for their operating system, and they are called Macintoshes, or Macs for short.
People will often say I run an Apple. Since Apple makes the hardware and the software operating system it's generally accepted to mean a Mac and OS X.

Microsoft does not currently make their own desktop computers. They leave this for companies like Acer, Dell, Toshiba, HP, etc.
These system all run Microsoft's operating system, Windows.

When someone says they run Windows, they are mean one of these hardware companies machines with Microsoft's Windows operating system.

PC officially stands for Personal Computer.
All home computers whether made by Apple (Macs), or the ones from the companies above, are PCs.

BUT, generally its common when people say PCs to mean a computer that is running Microsoft's Windows. (from Dell, Acer, etc)

The context in which the word is used should tell you which meaning is meant.

Ex.

A) I have a PC at home. (Windows Operating system. Although technically this it could be a Mac, most people with Macs would say they have a Mac at home.)
B) The development of the PC made many programs available for home users. (Any computer made for home use)

Hope that helps.