Circular orbits at different altitudes require different speeds, so if you start with a radial separation, the spacecraft and station will tend to drift further apart unless they accelerate themselves radially to close the distance. The effect is small at small distances, larger at long distances. To a first approximation, the separation is the difference between the force of gravity at the altitudes of the two. (Despite the frequent use of "zero gravity" and "microgravity", there's plenty of gravity in orbit -- about 88.5% of Earth's surface gravity, at the ISS' 400km altitude.)
At 20m of radial separation, this gravitational gradient causes the spacecraft and station to drift apart by about 50 micrometers per second squared - 5 millionths of a g. This is small enough that it can be largely ignored -- it is "lost in the noise" of thruster variability and inaccuracy of measurement of speed and distance. It can be counteracted with very small pulses of thrust, and the docking spacecraft can maneuver directly for its destination, i.e. with a radial burn.
At greater distances, the gradient is more significant. At 40km separation, the effect is a relative acceleration of about 0.1 m/s2, which is about the maximum that a loaded Crew Dragon could achieve firing 4 small Draco thrusters continuously -- it could just hold the distance and couldn't approach closer. So at distances like that, approaches are done by firing prograde and retrograde, Hohmann-style; you fire retrograde to lower your perigee by 40km, wait half an orbit, then fire prograde to circularize at the lower altitude.
Somewhere in the middle is a crossover point, where your pilot (human or computer) can begin treating the space between the spacecraft and station as "flat" and ignore the gravitational gradient. I believe the approach and docking process with the real ISS, which is more complicated than I'm going into here, defines a number of "hold points" starting at around 250m separation where the gradient is about 0.6 mm/s2; for a hold point to make sense, the gradient has to be small enough that you don't spend significant fuel fighting it.