Not necessarily. There are many "variations on a theme". Logic would be that you'd make whatever you're distilling, so as to be as clear and pure as possible. If you look "around the bazaars", you'll read and see pictures of many different variations of the same thing i.e. pot still or reflux still, method of heating (direct, steam, indirect, immersion element, etc etc), distilling on the sediment/mash/pulp, etc etc.
If you then either watch "Moonshiners", or just look up about it on the net, you'll see they often use the tank/boiler for fermentation and distillation, without removing the yeast or other corn debris. This does seem counter intuitive but it entirely depends on many factors, whether you end up with a nice tasting, quality product, or one that is more horrible than hell with a nasty burnt/scorched taste etc.
Hence don't be surprised to read, what seem like very strange methods of production, as well as a distinct lack of knowledge about what many of us mead makers do as a matter of routine. They just do some stuff differently to achieve, effectively, the same aim........
The fact that commercially produced "honey liquor" products are quite rare and regional, is likely about the increased cost of materials and higher cost of production of those materials............ Of the few available "honey liquor" or spirit drinks that have a honey flavour, I think you'll find that most of them are like vodka that's had honey mixed in..........