It depends on your definition of the word “Dollar Store”. If you use it to mean a store that sells goods priced in dollars, then yes. But there wouldn’t be many stores in the USA that aren’t.
I would argue that Dollar General is more of a general store: a store that sells a little bit of everything. They have a very limited selection of the top items that people in the area need or want most often. They have intentionally low price points, but their price points vary between $1 and $50. They do tend to price on the whole dollar ($4 instead of $3.97) or coin amounts ($3.75 or $3.50, not $3.49 or $3.69)
Technically, they do “fix” food deserts in that their model allows them to do business in locations with very few people who will shop their store. They have exceptionally low overhead and low staffing requirements. (And thus return little economic activity back to their community.) They locate their businesses in locations that have barriers to their customer base getting to a different shop; in rural areas, that’s a longer car ride, in urban areas that may be streets that are not designed for walking, intimidating anti-pedestrian features (like train tracks, rivers, highways, etc), or other areas where the average customer would find value in not going elsewhere, even though the selection is worse and the prices are higher.
I would not say they are a good fix for food deserts because they rarely stock unprocessed food. Most of their food is either frozen or shelf stable. I think almost everyone, including DG customers, would prefer to do their grocery shopping at a real grocery store with fresh food, meats, and dairy… but that takes more effort. So some will do the big shop at the nearest grocery store and buy forgotten or impulse things at DG; other people don’t have the resources to do that so they make do with boxed food indefinitely.
They have a very different marketing strategy. I doubt if anyone considers them to be the best store, but… they are right there, I don’t want to drive 30 minutes to the Walmart and spend that much time shopping, or I don’t want to walk the three miles and under the interstate with the homeless guys to get to target for my one thing.
The Dollar Tree, on the other hand, almost everything in it is literally speaking $1. That box of soap? $1. That bottle of pop? $1. Probably 95% of their SKUs are sold for the same price - one dollar. That is what I define a “dollar store” as. There is rarely a “captive audience” effect at the Dollar Tree, and I bet almost no one uses it as their primary store.
Dollar Generals are basically high priced, low selection convenience stores that stock more actually needed stuff. They are a half step up from a rural gas station’s grocery and T-shirt departments…
Dollar Trees are normally not located in food deserts, they are normally (at least in my experience) located in a shopping center near other retail.