When I hike, it is usually part of a backpacking vacation. Examples include the Grand Canyon in two days, Blue Mountains NP - a dayhike, even the Manhatten hike from Harlem to Battery Park, which I've also done in a day. In the UK, I hiked the Jurassic Coast Path, taking me a week to do this, and also the Hadrians Wall Walk, that is, from coast to coast across northern England. That took me four days.
You may have a different definition of backpacking to what I have. To me, backpacking is traveling independently, and usually on my own, from place to place with a rucksack for luggage, which is much more practical than with a suitcase. When I come across a venue which arouse interest, I can spend as little as a couple of hours up to as much as ten days. If the venue involves an overnight stay, I look for a backpackers hostel. More interesting venues have at least one, others have several within close range of each other.
Hiking for me is part of backpacking, as it involves going from one venue to the next. There have been times when I took a dayhike after arriving at the start straight from home, and returning home after the finish. In quaint English this would be known as Rambling, not hiking or backpacking.