Custom (cut and sew, OEM)
You bring the design, as a tech pack, sketch or reference, and the factory makes it to your specification. The design is yours.
Private label
The factory develops or adapts styles for you, often starting from its existing designs, and produces them under your brand with your labels and packaging.
White label
Ready-made generic products that several brands buy and relabel. Fast and cheap, but not exclusive.
Which suits you
If you have a design team, custom manufacturing gives you control. If you are launching quickly, private label shortens development. Either way, agree in writing who owns patterns and artwork.