I believe that colpitts is commonly used with crystals and most of the configurations below 20 MHz don't require inductors. It is an emitter follower configuration. The crystal provides the resonating inductance and the collector circuit need not be tuned as you usually take output from the emitter. However, if you want to pull harmonics from the oscillator, tuning the collector is done, with output taken from the collector. I've also seen harmonic colpitts oscillators that use an inductor from emitter to ground and take output from the emitter.
I have seen confusion in the past with the names of various oscillator configurations. Are we talking about different oscillator configurations?