One place where the distinction can become vital is in ER rooms. The following case was described (in another, closed, forum) by the chief on an actual ER: Suppose your ER is full, but you get a call about a patent in critical condition who needs an ER slot, and your ER is nearest. You have one slot occupied by a patient in a relatively stable condition, who could, with low risk, be moved to another ER, clearing the slot for the more critical case.
The utilitarian response is to accept the new patient, as the certainty of helping them outweighs the low risk in moving the existing one.
The deontological response is to refuse; you have accepted duty of care to the current patient, but not yet to the new one.
I don't know what a Virtue ethicist would do.
Actual ERs in the UK have different policies, depending on whether their ethics policy was written by a utilitarian or a deontologist. My interlocutor said that he would usually respond by the deontological rules, but in a crisis would (and in fact, had) act in a utilitarian way.