The rule is simple and it is kept strictly: a priest performs no sacred act without the epitrachelion. If the full vestments are not to hand, this one is, and a priest called to a sickbed, hearing a confession in a corner of the church, blessing a house or serving a short office will put on the epitrachelion over his cassock and nothing else. Where the other vestments belong to the solemnity of the liturgy, this one belongs to the priesthood as such, and its absence is not an informality but an impediment.
In confession it does a further piece of work. In common practice the priest lays the end of it over the head of the penitent while the prayer of absolution is said, so that the penitent is physically under the sign of the office being exercised.
The interpretations attached to it run in two directions at once. It is read as the yoke of Christ taken up, which is a weight, and as the grace poured out on the priesthood, which is a gift, and both readings are given in the same commentaries without embarrassment.
The Latin stole does the same work in a different shape, worn crossed or straight over the alb, and the atlas holds the two separately. They are counterparts rather than variants, and neither tradition would accept the other's form as its own.