Wal-Mart does deliver fast, because they have such a wide geographical area covered by their distribution centers, and they offer the option of picking up the goods at the store, sometimes available same day, just go to the service desk.
And they do have connections with outside vendors as well.
I find what I want on Amazon (easier search) and then copy and paste the description in Walmart to check the price. Often WM is cheaper and faster. My daughter loves one particular brand of body wash which is $18. a bottle on Amazon, she found the same on the Target website for $6.00. It pays to check.