I think I've said before a couple places, there are really three different things (at least) that people on BYC prefer to lump all together into the term "deep litter method".
One is the old-timey 'real' version, where you start with a bit of bedding on a dirt floor and just keep adding more gradually as the poo accumulates (possibly picking out the very worst spots, but usually not) until the cows don't fit into the barn no more and then you clean it all out and start over. This version produces meaningful warmth from composting, also can make the air more humid than you want, and while it works pretty good while the bedding is accumulating the stench when digging it all out is just out of this world.
Another is the same sort of thing done on a 'clean' floor (wood, cement slab, vinyl flooring) where you won't get anything like as much composting going on. IME with horse barns, the humidification of the air is less and the stench is not *quite* as amazing when cleaning it out, but it's similar in other respects.
Note that with both of the above, you start with only a 'normal' depth of bedding; it only deepens b/c you are adding more and more clean bedding on top as time goes by.
Finally, a lot of BYCers seem to use "deep litter method" to mean "I use a lot of bedding" but still clean it out on a regular basis, like weekly or monthly or every coupla months. This gives you none of the advantages of either of the other things, with the exception that yes there is deeper litter for birds to dustbathe in and snuggle down in on very cold winter days. It also goes through a lot more bedding.
I am not saying any of these is right and any is wrong, they are just different ways of doing things with different advantages/disadvantages.
Unfortunately I do not think there will every be any reliable semantic distinctions made between these things, on BYC, so it's just up to the reader to look at what's actually being said and categorize it accordingly.
Pat