It does vary depending on the student. With beginners you are just trying to get them to understand the movements. I generally refer to it as shaping clay. It’s not a finished product, your just trying to create a general shape of their swing.
The one I get from high handicap experienced golfers is “I want to be more consistent”. I hear this a lot. My job here is to help correct the big miss. Whether it is fat, thin, slices or hooks. What is the cause of the big miss. Many times it is a miss conception of how to strike the ball properly and the proper sequence of the swing.
With better players it generally comes down to specific things. Not driving it well, poor putting, wedge play not consistent. With the better players, they tend to be more specific with what they are looking to improve on.
With all my players I ask for their feedback. I tell them it is my job to give them a road map for improvement but it is their job to practice what we have discussed and then give me feedback on their results.