The difference between Computer and Desktop

When used as nouns, computer means a person employed to perform computations, whereas desktop means the top surface of a desk.

Desktop is also adjective with the meaning: designed for use on a desk or similar piece of furniture.

check bellow for the other definitions of Computer and Desktop

Computer as a noun (now, rare, chiefly, historical):

A person employed to perform computations; one who computes.
Computer as a noun (by restriction, chiefly, historical):

A male computer, where the female computer is called a computress.
Computer as a noun:

A programmable electronic device that performs mathematical calculations and logical operations, especially one that can process, store and retrieve large amounts of data very quickly; now especially, a small one for personal or home use employed for manipulating text or graphics, accessing the Internet, or playing games or media.

Examples:

"synonyms: processor [['puter]] q informa[[box]] q slang machine calculator"

Desktop as a noun:

The top surface of a desk.
Desktop as a noun (computing):

A desktop computer.

Examples:

"Laptops are often more expensive than desktops."
Desktop as a noun (computing, GUI):

The main graphical user interface of an operating system, usually displaying icons, windows and background wallpaper.

Examples:

"I installed a new application and it added its icon to my desktop."

Desktop as an adjective:

Designed for use on a desk or similar piece of furniture.
Desktop as an adjective (computing):

Of an application, designed to be run on a personal computer.