"So what do Europeans call hiking "
Backpaking is also the Aussie and Kiwi term for hostel to hostel/working holiday type travel.
We call hiking "bushwalking" and the Kiwi use the term "tramping" however hiking is universally understood even by the "hill walking" Poms (that is the English)

Most hikers have a pack larger than the cabin allowance so we check it in as luggage, usually wrapped up in a bag to avoid the straps getting ripped out.
Most luggage manufacturers have cabin specific bags (that is made to fit those measurements) including some that have backpack type straps.
http://www.ospreypacks.com/en/product/backpacking/farpoint_40