Hi Frinze and welcome to the forum,
To be honest, I wouldn't personally use a term like BDS, I think it's misleading. There is Dropshipping DS and then there is Blind Shippping, two different things essentially. Dropshipping (DS) is having a supplier engage you as an agent to sell their products on their behalf. So you do the marketing, then when you get a sale you process the order and they send directly to your customer without their branding, but send you the invoice.
Blind Shipping (BS) This is usually done between wholesaler and retailer, where a product is sent from the wholesaler direct to the retailer's customer, bypassing the retailer altogether. This can be requested by the retailer in an event such as an urgent back-order that their customer is waiting on, so it speeds up the delivery process for them.
In this case there may be branding and the customer may also get a copy of the invoice, although the price will be blanked so as not to give away the retailer's markup to their customer. (this is where the term blind shipping comes from)
So while some people do call Dropshipping BDS, I think DS (Dropshipping) is a far more concise term.
Were there any other terms you were unsure of?