Today the name is often applied to vehicles that are based on the same platform, but in many cases they are far from true 'rebadges'. Vehicles like the Chevrolet Silverado and GMC Sierra pickups often get called rebadged, but these vehicles feature unique exterior panels and interiors, so while the platform and overall shape is the same, they clearly aren't the same vehicle. The same goes for the Ford Fusion and Lincoln MKZ sedans, for example. There are enough differences in the bodies, interiors and options available that the rebadge moniker looses its meaning.
Since Mercury didn't exist in Europe, Ford chose to brand the Cougar a 'Ford'. In this case we have another true rebadge. The only differences in the car, aside from a few changes to the head and taillights and side marker lights for legal requirements (due to difference between US and European laws) are the Mercury-to-Ford badge swaps.