It's legally the same chemical, and often the same brand. However, their handling of potentially sensitive products is profoundly lacking. See: https://apnews.com/article/dollar-tree-lead-cinnamon-applesauce-wanabana-7376af3115d7fe506ad2cb168787d1d3

I wouldn't trust them to properly comply with a recall that I as a consumer would usually trust the store to handle, like taking products they know to be contaminated off the shelf. Additionally, I wouldn't trust them to ship or store those products in compliance with manufacturers guidelines.
Most things will be fine, but some things breakdown or develop issues if not stored in what are typically reasonable conditions.
For example, if kept too long or in improper conditions, aspirin can break down significantly and provide less benefit. Annoying if you're taking it for a headache, potentially dangerous if you're taking it for clot prevention.
Likewise bottled water, although typically drawn from municipal water supplies, is not held to the same standards and can develop bacterial growth if left in poor conditions too long.

Then there's the chronic staffing issues that can lead to food that requires refrigeration, like meat or dairy, to sit waiting to be put in the cooler for far, far longer than is safe.

Dollar stores are great for stuff like "I lost my shirt at the beach and I need something so I can go inside a restaurant", crayons, and general "stuff" you need only a small amount of and can afford the relative markup or only need infrequently. I wouldn't trust them for anything that goes inside a living creature because I have no confidence they even have enough staff to try to handle things appropriately.