I have been reading threads on components that have base management. What does that mean and how is it different from an LFE channel on a receiver that controls output by channeling the 80-120 hz sound to a subwoofer?
First, remember that LFE has nothing to do with bass. LFE is the name of the dedicated track on DVD that contains effects information that is band limited to just bass. So the LFE track is always the LFE track reguardless of bass management, if any.
What bass management really refers to is how a receiver deals with the low end of the frequency range since they know very few speakers are truly full range. Bass management can be as simple as a crossover at 80hz like you stated, but is usually more. Many receiver handle bass differently in different modes. In DD and DTS it is usually just the crossover at 80hz. Many receivers handle bass differently in stereo modes. Some will send bass to both the sub and the mains, which is called bass doubling. There are reasons for it, but most are opposed to that. Some will let you turn the sub off and run the mains full range for music. In that case, bass management is actually bypassing bass management circuits. Then there is the technical side of it. How the circuits manage the bass varies. Cheap receivers will do it all in one chip. Some receivers make a copy of the data and send one part to the decoder, and the copy to the bass management circuits, which is cleaner. If you are using analog inputs, then it has to be converted to digital for bass management. Some receivers will copy it and send the analog signal to the speakers, and convert the copy to digital for bass management. Some will convert the entire signal to digital, run bass management, and then back to analog. etc.. etc.. etc..
As you can see, it is a lot more than a crossover, and it has nothing to do with LFE.