Focal reducer, field flattener and telecompressor terms are all used rather loosely. Some telescopes have integrated field flatteners as part of the optical design i.e TV-NP101 has a two element objective at the rear.
There is some great information from Optec with raytrace and spot diagrams of their telecompressors.
http://www.optecinc.com/optec_026.htm
Fundamentally, they all operate the same, but you do need to pay attention to the focal plane distance to obtain optimal performance. In some cases, spacers maybe required. In addition to this, some products introduce vignetting as the focal plane is shifted.
Russ Croman has provided some excellent focal reducer positioning formulas that can be adapted to most telescopes -
http://www.rc-astro.com/resources/reducer.html
I guess the important point to understand is that using a focal reducer doesn't always mean your getting the advertised reduction. Rarely does an SCT roll off the production line at F/10 (as advertised). The old LX200's for example were actually F/10.7. Therefore this and other accessories can increase/decrease the effectiveness of the focal reducer.