The above are not in the proper format - the "http://" and "www" are not parts of the domain, but a server designation and parts of a URL.

Quoted from InterNIC's domain name registration instructions:

For second-level domain names under COM, ORG, NET, EDU, GOV insert the two-part name of the domain you wish to register, for example, ABC.COM. The total length of the two-part name may be up to 26 characters. The only characters allowed in a domain name are letters, digits and the dash (-). A domain name cannot begin or end with a dash (see RFC952).

As indicated above, a second level domain name can only contain two parts: the name itself (e.g. instantdomainname), and the category of the name (e.g. COM).

Now, lets see what's wrong with the first one: www.mydomain.com -- it seems to be OK, as it contains characters only and is less than 26 characters. However, it is still incorrect!.

For one, the dot (.) is not an allowed character. Though the above InterNIC instruction doesn't clarify this, a period can be used only when a subdomain name or a host name is attached to the main domain name. In the case of www.mydomain.com, www is a host name (typically the name of a Web server host). InterNIC doesn't deal with registering a subdomain name or a host name. These are handled by your own organization after your own primary domain name is registered.

The second one: http://www.mydomain.com is totally off the mark. It's a URL (Universal Resource Locator), server and path information used in HTML-coded source file to locate another document. Thus it's totally different from a domain name, though, sometimes people interchange the two in their daily vernacular. Nevertheless, a URL is not a part of a domain name, although a domain name is always part of a URL.