You can do all three activities in Nepal, but they are quite different things. Trekking is a multi-day walk, where you stay overnight (or several nights) at the place you’ve walked to. Hiking generally refers to a one-day walk. It might be two hours or eight, but if it takes place within a single day, it’ll probably be referred to as a hike. Mountain climbing is another thing entirely. It takes special equipment, training and comes with more risk. Neither trekking nor hiking requires any special skill, other than the ability to walk.