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.
Most travelers to Nepal choose to visit the country for the culture and some of the world’s best outdoor experiences. And, while Kathmandu is worth a visit in itself, many visitors simply spend a night or two here before taking off to other areas of Nepal. At least, this is what we did when we came to Kathmandu.