Tracking down the etymology of these nicknames was harder than I expected but I think AZCentral.com summarizes it the best:
https://healthyliving.azcentral.com/soccer-cleats-4560.html
The Difference Between Tennis Shoes & Sneakers
by Aline Lindemann
Sneaker, tennis shoe, athletic shoe, trainer ... these are all common names for a similar item -- a rubber-soled shoe that is worn for exercise and athletic activity. This kind of shoe is typically made of a combination of canvas, nylon and leather and has laces on the top of the foot. Although the various forms of athletic shoe or sneaker have the same origin, their purposes and specifications have evolved into a vast and diverse industry.
Lingo History
School boys of the late 1800s coined the term "sneakers" to refer to the soft-soled tennis shoes they wore that enabled them to sneak around. The "Boston Journal of Education" spread the word, and two years later, "The Boston Globe" began advertising tennis shoes -- flexible, non-marking shoes meant for playing tennis -- as sneakers. By 1895, the term "sneaker" began appearing in dictionaries.
Tennis Shoe Origin
Tennis shoes have been around since they were called Plimsolls in the mid- to late 1800s. These canvas and rubber shoes were worn while bicycling, playing croquet, walking and playing tennis. They were lightweight and flexible, and they were considered a luxury because games and athletics were pastimes for those who had time to play rather than work. As athletics have evolved, so have the variations of the tennis shoe, and although many shoes are marketed specifically to tennis players, this is still a common name for many athletic shoes, even those that never see a tennis court.
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I have used both nicknames, and have even used sneakers to describe the Converse brand back in the day, but I typically call them tennis shoes.