Production of a product could be manufactured with different technologies at different plants. Often production is measured by bussiness outcome parameters, while manufacturing is assessed by the product quality metrics. Both are result of Industry-Business Planning and Capital Investments. For example, large production of products is manufactured in China due to cheap labor cost. Naturally, the same products could be nafactured elsewhere, but the labour cost may be more expensive. As such, the business decision makers plan production manufacturing at the minimu cost.
In practice the two terms are often used to indicate the same activities i.e. the creation of an item using inputs of materials, labour and other resources. These can be products, processes, services, food etc.
The work manufacture is a verb and can be used to describe the conversion process outlined above, or biological processes i.e. plants manufacture their own food through photosynthesis.
The work production however is a noun. It is the name given to the act of manufacturing something or producing something from some type of process, which can be physical. chemical or biological