OK, those words: "director"..."spiritual direction"!!Makes me think of a traffic cop, music conductor or something else. This is certainly a misnomer because it implies we are telling others what to do, how to do it...directing...but this could not be further from what spiritual direction is. It is not even trying to point a person in any direction.
Other words have been used, like "companion" but I guess there's a problem with our English language no matter what word is used, so "spiritual direction" it is. As I continue to "learn" the art of spiritual direction, it is beginning to sink in that the spiritual director is actually a companion to those who come for direction. It is a journey with another, allowing that person (directee) to lead the way in conversation with focus being on spiritual things. I define spiritual as being our relationship with ourselves, others and God (not religious dogma, church rules/regulations, etc.)
Oh yes, if a question comes up that would assist the conversation in going deeper or would help expand it, this is appropriate especially if it "evokes" some deeper reflection and awareness. A good question "evokes" from the other something from within that person. This "Evocative Method" is what I have been trained in. It also trusts that the the holy/the divine is present, really leading the way.
So, nothing to get hung up on...whatever word you want to use, just remember, you are leading the way, not the director!