The bill of materials comes out of the takeoff. The takeoff says what the drawings show. The bill of materials says what to buy, with part numbers, sizes and finishes.
Example: an electrician counts light fixtures by type from the fixture schedule. The bill of materials lists each type with its catalog number, lamp and mounting hardware.
Build the list from the schedule and the spec together. The schedule gives the type and count. The spec gives the options and accessories. Send the list to suppliers for pricing, and keep it to place orders after award.