The primary difference between Rankine and Coulomb earth pressure theories is that Coulomb's considers a frictional retaining wall. In other words, the interface between the soil and the retaining wall is not assumed frictionless (as it is in Rankine theory).
That being said, it is typically considered that Rankine underpredicts the true orientation of the failure surface, whereas Coulomb overpredicts the orientation. In that sense, you could use both methods, and use the two solutions to bound what will likely occur.
Terzaghi (and Peck)'s method is largely empirical. It simply uses the soil's classification and the backfill slope, then they simply tabulated coefficients of lateral earth pressure. That being said, they aren't bad, it's just that any empirical solutions like this tend to be relatively site specific, so the solution needs to be taken with a grain of salt.