The key difference between Manufacturing vs Production is that Manufacturing is the process in which raw material is converted into the tangible products, whereas, the production creates utility as is the process in which article is made for the purpose of the consumption by combining the different resources.

Manufacturing is the process where machines produce goods from raw materials. Production is the process of converting resources into finished products.
Manufacturing includes the production of goods which can be immediately sold off and are suitable for use. Production essentially means the creation of utility.
In the case of manufacturing, the use of machinery is mandatory, whereas, in the case of production, machinery is not essential.
For manufacturing, the output is tangible, whereas in production, the output which can be tangible or intangible.
In the case of manufacturing, both labor and machinery setup is mandatory, but in the case of production, only labor is necessarily required.
All kinds of manufacturing are considered to be produced, but all types of production are not considered manufacturing.
For manufacturing, the result is essential goods, but for production, the result may be goods or services.
In the case of manufacturing, raw materials need to be procured from outside. Whereas in the case of producing, the raw material is processed for getting the output, and procurement of raw material is not required.

What is Production?
In economics, a “Production” function relates the physical process to physical inputs or factors of production. The transformation of inputs into outputs, with added value, is called production. The primary function of production is to address efficiency in the use of factor inputs in the function of production. Production means the conversion of resources of nature to finished goods to satisfy the human wants.

Production is actively directed towards the satisfaction of the wants of people by converting physical inputs to physical outputs. The conversion can happen manually or with the help of machines. For example, we convert cotton to cloth, and for personal satisfaction, convert them into dresses.
The intangible services like service of the doctor, lawyers, etc. come under the theory of production in economics. So both tangible and intangible services are included in the production.
Production does not imply the creation of a matter. Production means creating utility out of the available resources. So production involves the creation of what the humans want from the available resources or raw materials.
So we can define production as the process through which a firm transforms inputs into outputs. It is the process of creating goods and services with the help of factors of production or inputs to satisfy human wants.


https://www.wallstreetmojo.com/manufacturing-vs-production/

ze wzgledu na przytaczane tu w tle - natywne opinie, że "manufacturer" brzmi wspolczesnie dowcipnie lub dotyka czasów 19-wieczniej rewolucji przemyslowej - proponuje spośród synonimów obu wyrazów - takie rozwiazanie:
wytwórca - maker
producent - producer

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Note added at 16 hrs (2021-07-25 11:24:16 GMT)
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wydaje mi sie, ze - maker - w kontekscie -- jest najbardziej uniwersalną reprezentacją wytwarzania;
- nie budzi wątpliwosci, że trąca anachronicznym znaczeniem;
- wyznacza tradycyjną w j. angielskim kardynalną prostotę nazywania rzeczy, co jest niewątpliwie atutem w posługiwaniu się j. angielskim -- współczesnym - lingua franca - zeby tak jeszcze na koniec - pobrylować ;)