The One-Step, which emerged as a distinct style around 1913, was so called because it was just walking to the music. It had certainly been something people were doing well before it became "a thing", but its arrival on the scene was a pretty big deal.
It was popularized by the social dance power couple, Vernon and Irene Castle as a respectable, socially acceptable alternative to the rowdy and unruly Turkey-Trot, and it made it socially acceptable for the more conservative to get up and dance to the new music.
It took many forms, and frequently devolved into just shuffling along. The Castles promoted a style they called "The Castle Walk" which was a fast moving, kinetic style. The first video will show that style. The others will show some other takes on it.