B737 Captain reported a miscommunication with the ground crew during push back procedure resulted in the aircraft rolling forward towards a tug uncontrolled.

Narrative

During push back the aircraft became detached from the tug. There was no indication such as 'breakaway; breakaway'; or two-step alternating alert tone'. There was no communication from the pushback crew at all. During the push back the aircraft was moved to a spot as would be normally expected. We were given the 'cleared to start engines' instruction; and then the aircraft came to a stop for a moment or two. Then we started moving forward again. A ramper appeared aircraft left holding up the lockout pin; and the tug was moving forward away from the aircraft. I realized what had happened and smoothly applied the brakes. I am aware that ZZZ is primarily served by RJs and I am not sure if the ramp crew are [company] employees or not. I suspect there could be some differences in SOP from mainline aircraft and regional aircraft. However; I cannot stress enough the need for standardized communication in this process. We were never given the 'set brakes' command; which led me to believe we were still under tow. When in fact the ground crew had disconnected the tug; lockout pin and headset. The obvious danger here is we were rolling forward and the tug was backing up. To my vantage point; that looks normal; like we were still connected. The reality was the tug was reversing because it was trying to get away from the aircraft. We were fortunate to avoid damage or injury."