A self-propelled particle is a basic ingredient of active matter. Any handle on its noise characteristics is thus of both fundamental and applied interest. In this paper, we show that geometric constraints are a route to affect the emergent noise properties of a single active particle, thus demonstrating that seemingly different active particle classes are equivalent to each other. Specifically, we find that the chiral active Brownian motion of a self-propelled particle seen in two-dimensions switches to a run-and-tumble like motion when confined to a quasi-one-dimensional channel. Our analysis of this switching behavior connects the resulting active stochastic dynamics to that of a two-state molecular motor. The emergent tuning of active noise characteristics by unbiased external driving, as we demonstrate here, is illustrative of generic mechanisms of active noise control in other systems.