The two fluids are very similar but the additives are different because they do different things. It's unlikely anything will be damaged but your transmission uses a special transmission fluid with the correct additives to prevent a shudder during up-shifts and torque converter lockup. I'd probably pursue a transmission filter change and flush to be safe, but I don't think I'd lose sleep over it.
It's the brake fluid you don't want to get any hint of a petroleum product in. That can cost more to repair than a 10-year-old car is worth.