The priest’s stole is worn around the neck, like a yoke. The deacon’s stole is slung across one shoulder and the opposite hip. The stole is a “sign” or “badge” of office. The liturgical vestments (alb, stoles, chasubles) indicate the positions of service to the community provided by bishops, priests and deacons.
Many cultural realities have something analogous to this. Various indicators of captains on sports teams are ubiquitous (e.g. the arm cuff worn by one player on each side during the World Cup).
Father Edward McNamara, professor of liturgy at the Regina Apostolorum Pontifical University writes: “In the light of the Second Vatican Council’s call for an overall simplification of the rites and rubrics, this distinction in the way of donning the stole [between bishop and priest] was abolished. The present indication is that all bishops and priests wear it hanging down in front” There’s more at this link.