They both are turbo charged, have an ST badge and made by Ford.
Thats about it really. I'm in the grumpy camp that doesnt like the ST badge on non-car models. The Edge is not a hot hatch but I would say more of a continuation of what Ford previous called Sport. Dont get me wrong, i like that Ford is upping the HP for their other models but its not gonna be the same. You arent going to find a bunch of the Edge's on autocross/racing or being the darling of the car mags like the Fiesta and Focus. It's just Ford cashing in on the nameplate and marketing that is already out there for the ST. I understand why they are doing it, i just disagree.