Rebranding
Can actually work in a variety of ways, one of the most common being manufacturer A asks manufacturer B to make X number of products for them, with whatever modification it is they require - such as a specific colour, name, or whatever.
Manufacturer A then buys them off maunfacturer B. Job done. No profits shared, nothing, just a straightforward business to business transaction. The downside for manufacturer B is that they will have to sell to manufacturer A for a lot less than they would have done had they sold directly to a supplier. They also stand to lose sales of their regular lines when manufacturer A puts their goods on sale as a consumer may well choose the product of manufacturer A over manufacturer B.
The upside is that it's a done-deal, it's in the bag, a run of, say, 30,000 vacuum cleaners, money is in the till so to speak, and they don'ty have the worry if it's a poor seller.