I had to edit the original question because I sensed that there were two questions being asked. I think that Stevens' distinctions about what it means to be a butler play a formative role in his own self definition. For Stevens, his life as a butler to Lord Darlington is one in which absolute loyalty to one's master is what defines both personal and professional domains. This adherence to loyalty is something that Stevens' own father displayed in his professional service. For this reason, Stevens and his father possess little in way of difference of how they cast themselves.
The distinctions that both men make are ones that silence personal lives and personal preferences to the concept of duty and loyalty to the people they serve. It is for this reason that they are not able to reconcile with one another on a personal level. Stevens' father's own professional demeanor eliminated the room for personal emotions. Stevens, himself, embodies the same reality. There is little distinction between both men. Stevens himself does not distinguish between loyalty in service to a master and his own sense of voice. He is "unable to be of assistance" in anything that does not involve absolute obedience and service to his master. Stevens' distinctions that suggest his only purpose is to serve someone else and silence his own voice are representative of both the life he has led as a butler and form the basis of his arc of reflection about the choices he has made.