Dollar Tree is an actual "dollar store" where literally every item costs $1. Dollar Tree's items are generally no-name discount brands that wouldn't be found in big grocery store chains, or familiar brands in unique very small packages.
Dollar General, at least in the two parts of the US I've seen them in (areas of California and the Midwest), is as you describe: something between a convenience store and a traditional grocery store sans produce. They have all the normal big brands: Oreos, Doritos, etc. in the normal package sizes at what seemed to me to be normal grocery store prices.