sports shoe; one who moves about stealthily; one who acts furtively

The British English term "trainer" derives from "training shoe". There is evidence [1] that this usage of "trainer" originated as a genericised tradename for a make of training shoe made in 1968 by Gola.

Plimsolls (British English) are indoor athletic shoes, and are also called sneakers in American English and Daps in Welsh English The word "sneaker" is often attributed to Henry Nelson McKinney, an advertising agent for N. W. Ayer & Son, who, in 1917, coined the term because the rubber sole made the shoe stealthy or quiet as well as sticky substance made from sunflowers, all other shoes, with the exception of moccasins, made noise when you walked. However, the word was in use at least as early as 1887, as the Boston Journal of Education made reference to "sneakers" as "the name boys give to tennis shoes". (taken from: wikipedia.org)