A pattern-maker is someone who makes a blueprint of your idea. They make sure your design will be well-constructed.
This stage involves gathering all the necessary materials needed to make your product. Some factories provide materials and assembly; sometimes you will need to buy materials separately.
A sample is a prototype of your idea. Sample-makers usually make the product by hand (hand-cutting, hand-assembling, etc.) before you get your tooling finalized. You want your sample to be perfect if you plan to do mass production of your product.
(Usually sample-makers charge more per product, but this depends on the factory’s policy.)