Well, yes and no. Many brands are owned by the same parent company and even some that aren’t will share technologies, parts and manufacturing facilities.
In fact, this is more obvious when you compare race skis. If you put a Nordica next to Blizzard, you’ll notice that besides the graphics, they look almost identical. Not only will they take the same bindings, the protective tip will be identical on a slalom ski. Same for Head and Fisher share parts and binding compatibility. In some cases, one brand (eg. Rossignol) IS the parent company and owns outright another brand (eg. Dynastar). Rossignol and Dynastar both use Look bindings. Who owns Look? Rossignol.
To be honest, this is a good thing for us parents, because parts are interchangeable and more importantly, bindings can be re-used when your kid outgrows one pair of skis, saving you money.