Sawyer is a specific term used for the person who abundantly saw the wood particularly by using a pit saw. But It is not a thumb rule the person can use or operate the sawmill as well. Such jobs are particularly defined for the people who cut lumber particularly to be used by the consumer market. ThIs task is mainly done by the people at the end point running the business of the lumber or the people at the home improvement stores.

In the logging industry, the term is still used interchangeably for the person who operates the chainsaw,wildfire suppression, harvesting, trail construction. On the other hand, the construction industry used this term for a separate person, the person who is responsible for operating the concrete saw.

https://en.wikipedia.org/wiki/Sawyer_(occupation)#:~:text=Sawyer%20is%20an%20occupational%20term,ground%20or%20operates%20a%20sawmill.&text=In%20the%20construction%20industry%2C%20the,operator%20of%20a%20concrete%20saw.