Yes
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A laptop can be a PC, but not all PCs are laptops. (see rectangle to square relationship)
Really though,
A Personal computer can be configured as a desktop or laptop, but also implies that it's running a Windows operating system. Laptops also exist as Mac's running OS X or Snow-leopard and made by Apple.
No, a laptop you can take with you and a computer is stationary.
--12/23/10 Update:
Technicality, I would say that a laptop is a type of computer. A stationary computer is sometimes called a "desktop computer."
--Julian B.
Yes. Laptops and Decktops are PC's.
PC means Personal Computer.
All Mac's, any Windows computer (Dell, HP, etc,) and Linux computers are technically PC's.
If your talking about computers in general then PC is fine. If your talking about specific computers then it's usually OK to differentiate between them.
I've got a Mac or I've got a Dell, HP, Vizio computer are examples.
A laptop PC is a personal computer that has been shrunkdown to a smaller size for convenience and mobility as well as portability, one that would fit on someones lap" hence the term "laptop"