It's just a detail, but no matter what bike you have, the gearing system is all the same. It's either Shimano or Campagnolo, and the shifting levers are a bit different, and you can have a double or a triple, etc. but the technical stuff is all the same in the end. The same type of gears on different bikes should work the exact same way. Conversely, the same make of bikes (ex: Trek), and even the same model (ex: F7500) can come with many different types of gears.