Both White label v/s private label products have been always a part of the debate ever since the eCommerce industry started to flood with sellers.
In a general sense, private drop shipping is done by those sellers who own exclusive rights of the products and source it directly from the manufacturer who has agreed to their specific details.
Whereas white label dropshipping is the usual dropshipping route where you sell pre-made products where there are no customizations available and you buy a generic piece from the manufacturers and sell it as your own brand.