OEM means the factory makes your design; ODM means you choose from the factory's designs and put your brand on them. ODM is faster and cheaper because the tooling and moulds exist. Most new brands start ODM and move to OEM as volumes justify tooling.
Minimum order quantities run from about 300 pieces per style and colour for acetate and metal in China's better factories, higher for injected frames because of the mould, and lower for Italian and Japanese workshops at a much higher unit price. Sampling takes four to eight weeks; bulk production sixty to ninety days.
Specify everything in a tech pack: materials, colours, plating, hinges, lens type and treatment, markings (CE, UV400, size), case and cloth, packaging and barcodes. Agree an inspection standard (AQL) and use third-party inspection before shipment. Payment is normally a deposit against order and the balance against shipping documents.