This really belongs in the tech forums, not here, as it is very important & has actually been discussed before.
However, it appears it is time to do it again as it often comes up.
Firstly, the LFE channel (or the .1 as it is called) is not the same thing as a subwoofer channel. Please read - carefully - the attached document from Dolby Labs.
View attachment LFE.pdf
5.1 refers to the channel count in a mix - 5 main channels, and an extra channel (the .1 is discrete, and is a 6th channel, but is called .1 as it takes up approximately a tenth of the bandwidth of a "normal" full-range channel.
The purpose of the .1 channel is to extend the bass response below 20Hz.
The purpose of a subwoofer is to reproduce frequencies the other speakers cannot reproduce, and depending on the system the crossover point can be as much as 250Hz and even higher, and is used in sub/satellite systems and the output will as a result always be a compromise because both the subwoofer and LFE channels are non directional. SO, to use an example, if you have a mix that is a true 5.1 mix, played back on a sub/satellite setup, you may well have phasing problems caused by the system being used re-routing bass from the 5 main channels into the sub, which will automatically conflict with LFE channel content. Depending on the phasing, you may gain or lose bass content and any bass content that was deliberately panned in the mix will lose all that effect rresulting in a very odd sounding mix. Bass Management needs to be set up carefully. Very carefully.
5.1 does not necessarily mean DVD-A, but 5.1 mixes can be authored to DVD-A. DVD-A can take any channel count from mono (not advised) to 5.1 and just about anywhere inbetween including 3.0 as L/R/S and L/C/R as well as all main channels plus the .1, the correct usage of is down to the mastering engineer to deal with.
