There's a lot to unpack here.
First, sellers are supposed to give the location of the product,not the location of the seller. Some sellers who are dropshipping (a lazy way to sell) don't understand this or don't want to understand this.
Some Asian companies have set up warehouses in the USA and ship from there. Your payment may go to China (or Singapore or India or South Korea) but your item will in fact be shipped from the USA.
AZ is a seller. They compete directly with the private sellers who use the site. EBay only provides a venue where millions of sellers can advertise. AZ has much more control over the products on the site, since they own them. If you want mass produced stuff, AZ has it, while eBay sellers will offer very competitive pricing. If you want out of production or collectible items eBay has the edge.