Running shoes
Running shoes are designed for forward motion, with an emphasis on protecting the front of your foot, heel, and shins. Because running shoes are designed for only forward motion, they have rigid sides to protect your feet. In pickleball, you are moving side-to-side and will need a shoe that will allow more flexibility ont he sides.
Because of this, running shoes are probably the worst athletic shoes you can wear to play pickleball.
Tennis shoes or sneakers
There is a regional difference between the terms “tennis shoes” and “sneakers” — but they are the same type of shoe. Tennis shoes are built to allow you for quick side-to-side movements.
Because you will be moving similarly in both tennis and pickleball, tennis shoes can be a good option for pickleball.
Cross trainers
Cross trainers are shoes built for more than one sport. If you can find one that is built to include tennis movement, meaning it is meant for side-to-side support, then a cross trainer may make an acceptable pickleball shoe.
Walking shoes
Walking shoes are lightweight, and are usually made with shock absorption. Shoes for walking put an emphasis on rigidity in the front, rather than the sides, and will help you move more quickly from the heel to the toe.
Walking shoes are going to be better than running shoes to play pickleball, but they are still not the preferred shoe for pickleball.
Trail running shoes
Trail running shoes are built for running on a number of different uneven surfaces, so will have some side-to-side support, which is good for pickleball. However, it will also have a heavier tread because you might be running in many different surfaces, like dirt, mud, grass, concrete, water, and rock.
Pickleball shoes
Pickleball shoes are of course going to be the best shoes to play pickleball. As pickleball gains popularity, more and more companies are making pickleball-specific shoes. Companies like Nike, Skechers, K-Swiss, Asics, New Balance, and others have their own pickleball shoes.
If you want to improve your pickleball game and avoid injuries, pickleball shoes are always going to be your best option.