Difference between a Domain,Work group and Home Group?

In a work-group:

@ All computers are peers; no computer has control over another computer.

@ Each computer has a set of user accounts. To log on to any computer in the work group,you must have an account on that computer.

@ There are typically no more than twenty computers.

@ A workgroup is not protected by a password.

 @ All computers must be on the same local network or subnet.

 In a home-group:

@ Computers on a home network must belong to a workgroup, but they can also belong to a homegroup. A homegroup makes it easy to share pictures, music, videos, documents, and printers with other people on a home network.

@  A homegroup is protected with a password, but you only need to type the password once, when adding your computer to the homegroup.

In a domain:

@ One or more computers are servers. Network administrators use servers to control the security and permissions for all computers on the domain. This makes it easy to make changes because the changes are automatically made to all computers. Domain users must provide a password or other credentials each time they access the domain.
@ If you have a user account on the domain, you can log on to any computer on the domain without needing an account on that computer.
@ You probably can make only limited changes to a computer's settings because network administrators often want to ensure consistency among computers.
@ There can be thousands of computers in a domain.
@ The computers can be on different local networks.

To find out if your computer is on a workgroup or domain

@ Open System by clicking the Start button , right-clicking Computer, and then clicking Properties.

@ Under Computer name, domain, and workgroup settings, you will see either the word Workgroup or Domain, followed 

To find out if your computer belongs to a homegroup

@ Open Network and Sharing Center by clicking the Start button , and then clicking Control Panel. In the search box, type network, and then click Network and Sharing Center.

@ If you see the word Joined next to HomeGroup, your computer belongs to a homegroup.

Source : MSDN