I don't think there is a lot of standardized terminology when it comes to backyard chicken keeping. Some terms have established themselves over time via use on the internet, and I guess maybe books too, but they get confused all the time. For example, "deep litter method" has come to be understood as one specific method, not just any litter that is deep and stays in place. The Deep Litter Method in chicken discussions refers specifically to compostable litter that is kept moist and encouraged to break down and compost over time. It requires the right balance of carbon (litter matter) and nitrogen (poop), the right amount of moisture, and aeration - either by the chickens or the humans stirring it. It's tricky to do right, without ending up with smell and filth, so what a lot of people end up doing instead is the dry equivalent of that - the "deep bedding method". That is a different thing. It's dry and does not compost, and the point of it is for the bedding to absorb the moisture and dry the poop out, because when poop is dry, it doesn't smell or cause sanitation issues. In the dry bedding method, you start out with a thick layer of bedding, and as it gets poopier over time you add more fresh bedding on top, until eventually you do a big clean and shovel it all out. The litter used for this method is usually organic materials (in the chemical sense of the word - organic as in derived from living things like plants, not "organic" in the fancy contemporary meaning of the word as in "raised without chemicals"). I guess technically you could use sand for this, but not for the composting "deep litter" method.
A lot of people use sand in the coop, but they are committed to scooping it regularly. So if you choose sand, you have to stay on top of it and do a lot of cleaning, because it won't compost and it won't absorb, and can start to smell. It's compacted a lot more densely than, say, pine shavings which have a lot of surface area, so wet sand dries very slowly. And it will freeze in the winter. Even if you scoop every day, by the time you get out there in the winter to scoop, the dirty areas will already have frozen solid into slabs of poop concrete.
Another problem with sand is that you have very limited options for what to do with it when eventually you need to do a big clean-out. If you have a lot of land, and very clay-heavy soil, and heavy equipment, you could dump it out there and mix it with the soil, but that's a lot of hard work - sand is heavy; getting it out of the coop will be physically harder than shoveling lightweight shavings; transporting it will require heavier equipment; and digging it into clay soil, at that volume and without turning the soil too sandy, will be a lot of hard work too. And eventually you will have to take it out of the coop, because you can't clean all the poop out - some will dry out and get pulverized into poop dust from the chickens walking/scratching and grinding it down. Over time, the proportion of poop dust to sand will increase, and the poop content will just stay there indefinitely because it won't compost.
Overall, long term, it's more trouble than it's worth. I highly recommend pine shavings or something else that's compostable - either in the coop with the DLM, or outside once you shovel it all out. I personally use the deep bedding method with pine shavings, and am very happy with it. I do a big clean-out twice a year, and the bedding isn't too heavy to shovel at all (unlike sand). I start out with a deep layer of shavings, which have a high surface area and dry quickly. It absorbs moisture and dries out the poop. I periodically add fresh shavings on top, with some PDZ, maybe once a month. Beyond that, I don't do any other cleaning. We have cold winters and it has never frozen solid. It doesn't smell. When I shovel it out, I put it in a compost pile behind the coop where it sits for half a year to a year, at which point I bury it in my garden. This has been working really well for me and I highly recommend it. But with any type of litter, how quickly it gets dirty and how/when you clean it out will depend on the density of chickens per square area. I stay at or under the recommended 1 chicken for every 4 square feet of area, and it has been working great. I have, temporarily, had more chickens than that in the coop, and oh man can you really feel it! It gets dirty much faster and breaks my nice balance.