A B777 Captain reported they released the parking brake at the gate but were not hooked up to the tug and the aircraft rolled backwards.

Narrative

The tug driver called the cockpit stating he was ready for brake release and push back. The cabin was not ready and I told the tug driver to standby. About three minutes passed when the purser said the cabin was ready and closed the flight deck door. The before push back checklist was completed. I released the parking brake; told the tug driver the parking brake was released/standby; and looked at the First Officer telling him to call for push clearance. The First Officer looking in my direction was the first to notice and announced that the aircraft was moving backwards. The time from when I said parking brake released/standby" to unintentional aircraft movement was immediate but slow. I thought the tug driver had started the push back without a clearance and I was trying to reach him on the headset. A few seconds passed when the tug driver immediately started saying "set brakes". I slowly applied brakes and set the parking brake. The aircraft rolled backwards about 5 feet before start of brake application and total movement was approximately 10 feet. There was no damage to equipment or injury to personnel.A new tug driver explained what happened. He informed me that the wrong tug for pushing a 777 was initially hooked up to the aircraft. The original tug driver noticed the error after his initial call for brake release and push back. He did not inform me of the need to disconnect the aircraft from the original tug to swap to the appropriate tug. If he had I never would have released the parking brake. I thought the tug was connected and ready for push. The airplane was not connected and when I released the parking brake. We started moving backwards within a second or two in a very insidious manner."