Unfortunately, Walmart has integrated a 3rd party marketplace onto their site too; so who knows when they will start fulfilled by Walmart and comingling. There's also persistent stories of Walmart demanding lower priced items and being ok with the lower quality, not always with different UPCs.
The funny thing about Walmart 3rd party, is it always seems to be drop shipped by a competitor, and comes in a clearly branded box. I've gotten boxes from Newegg, Target, Wayfair, and even Sam's Club.
Still a better option than Amazon (for now, at least).
This is the legacy Wal-Mart took over by acquiring Jet.com in 2016. They were a brand new site with millions of products in their catalog, yet didn't actually stock a huge portion of them. When I bought a wifi router from Jet, they simply ordered it for me from the Newegg website, and paid Newegg more than I paid Jet. It arrived in the Newegg box with the Newegg invoice.
I can buy Sam's Club brands and/or sizes first party through Walmart.com, and I could do so before the Jet.com-ification of the Walmart website... it just wasn't well known until recently.
I know... that's part of what makes it so interesting.
There are still 3rd party sellers somehow selling Walmarts own product cheaper via Sam's Club. Or sometimes for products that aren't available on both public facing sites. (Sam's and Walmart)
Which is probably why Walmart made the effort to better integrate the brands.
