A stop limit order is just a limit order with a stop that triggers the limit. If the limit is marketable it functions *like* a market based stop. However, this distance between what the best bid/ask is and the limit itself is where price banding gets involved. For instance, if you have a stop limit buy order that gets triggered, of which you prearranged with 10 ticks of payup, it won't be an issue. However, if you were to set the payup to be 100 ticks, it'll get rejected when the stop is triggered because that's outside the band in most cases. Why set any payup at all? Because maybe you don't want to have your limit sitting there when the instrument skips over you during periods of high vol. In this case payup would be "stop limit buy, stop/aux: 2080, limit: 2084" - if 2080 is hit, send a limit buy for 2084 (which will of course execute at 2080.25 if the market is 2080/2080.25).
With CME atleast, when you send a market stop it gets converted to a stop with protection which is really what everyone just wants to use anyway for tight/liquid instruments. Some people use stop limits in all cases. I do, because IB holds stop market orders on their servers (check the blue color, that means it's on their servers) and based on a few cases last year where I got my face kicked in by 10-40 ticks of slippage in crude and gold smash and grabs, I prefer my orders to sit at the exchange in all cases (which a stop limit will, as it's native) so there's one less round trip (and btw it *has* made a difference in some cases).
In other cases, when you're dealing with instruments which might be as tight or liquid or usually have a spread, one might desire to set their limit to not have any pay up but instead go mid-point if the stop is triggered. While there's no way to determine mid at that time, a few ticks or so might be what is desired - a few ticks meaning: if my stop is hit, I'll have the limit be 3 ticks back from what I would have payed if I hit just hit the bid/ask.