COMMAND.COM is the program that serves as the DOS command processor, or the DOS shell if you prefer. Like any operating system, DOS itself is simply software, albeit software that has a very special role in running your computer. Dos consists of a conglomeration of programs, utilities, and device drivers, but at its core are three key pieces of software. They must be present on the disk you use to start your computer, or the computer won't work. Of these three pieces of software, the only one you're likely to run across is COMMAND.COM-you'll see it in the list of files on your screen when you display the directory of that start-up disk, by typing DIR and pressing Enter. (The other two essential DOS files are hidden files, so you won't see them in the directory list.)
Despite its importance, COMMAND.COM is an ordinary file, just like any other file on your disk. You can copy it to another place if you like, but whatever you do, don't erase (delete) the COMMAND.COM file, and don't move it to another directory or another disk.
COMMANDC.OM is responsible for displaying the DOS prompt (like C:)). But its main job is to interpret the commands you type at the prompt (on the DOS command line). That is, when you type a DOS command and press Enter, COMMAND.COM "reads" what you typed. It figures out what you want to do-copy a file, display a directory, run a program, etc.-and then goes and does it. That's what they mean by "command processor." (By the way, it's possible to substitute another command processor for COMMANCDO. M; see the entry for 4DOS.)
In the technical sense, COMMANDC.OM is a shell, in that it provides a user interface, a way you can get at DOS'S functionality. But ordinary people use the term shell to refer to a program that lets you manage files and start programs without having to type commands-in other words, without interacting with COMMAND.COM.