There's really no consensus on what some of these job titles mean. IMO if it has "engineer" in the title, you're doing more than just writing algorithms. I'd

There's really no consensus on what some of these job titles mean. IMO if it has "engineer" in the title, you're doing more than just writing algorithms. I'd say that in your example, Company 1 was looking for a developer or programmer, whereas the other company was looking for a software engineer or product engineer. Also, IMO the term "Product Engineer" does not denote that it has to be software-related at all. It could be someone who designs shoes or training seminars or whatever (see https://en.wikipedia.org/wiki/Product_engineering https://en.wikipedia.org/wiki/Product_engineering).