Self regulation and attention are closely tied.
Self regulation requires attention. Suppression requires attention to the thought being suppressed, and any kind of conscious regulation requires attention to the thing to be regulated.
Attention also requires self regulation. Thoughts must be corralled, kept relevant to the task at hand. Physical motions must also be kept together. In a classroom, this means staying in the seat, focusing on material, not falling asleep. In a car, this means controlling pedal use, steering, signalling, and keeping eyes and thoughts on the road. On a sidewalk, this requires only avoiding other people and maintaining the process of walking forward.