Assume the approximation that the Earth is spherically symmetric — without higher order gravitational multipoles, and other effects that might be related to gravity from other bodies or the Earth's orbit around the Sun are ignored. Given a circular orbit, "down" would be a vector pointed towards the center of the Earth, and I think the "nadir" would be in exactly the same direction.
But in a realistic circular orbit, do "down" and "nadir" have any more nuanced meaning by convention or usage?
For example, there is a vector that is perpendicular to instantaneous velocity and orbital angular momentum, another that is the local gravity gradient, and yet another that points towards the Earth's center of mass.
All of these could be thought of as roughly "down" or in the direction of the "nadir", but are any of these (or something else) used preferentially or by convention?
note: This question is asking a lot more than just What are these orientations called in orbit?