merchant fulfilled - this is where you hold the stock and ship it to a customer directly. when you do this, you do indeed get the customer's name and address

fulfilled by Amazon - this is what most people do and it's when you ship the stock to Amazon's warehouse/s and have them do all the logistics. this is how products become prime eligible generally and in this case, amazon shares no order data with the customer. amazon is very protective of customer data as they want to milk it themselves lol,

If you sell using a print-on-demand model, you use a different amazon site called Amazon called Merch by amazon (not Seller Central). In this case, you upload image pngs to amazon and can select what merch it goes on. amazon then pays you a commission when a sale is made and does all the logistics, but you don't even see any customer info, and have no way to even contact any customer.