Googlemail is not different; it is the mail solution trademark for certain countries where the Gmail domain wasn't available. Let's have a quick test. Open you email account, other than the one provided by Google, let's say Yahoo. Login to yourID@yahoo.com and send a mail to your Gmail/Googlemail account but instead of your domain, write the other name (Gmail for Googlemail and vice versa). Check your Google account. The mail is here, isn't it? That's why I'm saying they are the same, so stop requesting a different domain.
As you know, Gmail is the mail solution provided by Google and released in 2004. Since the official launch of the product, it was till recently available only by invitation, no free registration being allowed. Starting with February 2007, the search giant decided to make it a public beta and made it available for free for all Internet users. Although it was only a private product, Gmail managed to gather a huge number of clients because every user was able to send no more than 100 invites to his friends.
When Gmail was released, Google described the service as the mail solution with the largest file storage size, offering approximately 1 GB. Then, it evolved and received a lot of new features and functions, all of them included in the freeware product available today. Now, Gmail is regarded as the most secure mail service because it is able to filter the spam messages sent from any address. Keep rocking Google!!