(I'm aware that there's been some effort to extend the legal significance of the word "engineer" to the software industry, but I'm curious if that difference is actually in practice anywhere today)
Engineer invokes a sense of design, but so does programmer. When I started, there was no job where you just coded straight pseudocode specs. Business described the problem the way business does, and you had to convert that into a computer solution. Within that solution, different developers would own various parts of it.
I would say the entire process of having coders who design systems and coders that just write code is inherently broken. Businesses want to think of development as prod-ops, but it's more like book publishing. I'm of the mind that if a coder who designs a system in enough detail to write pseudocode, he should just write the application.
The better approach is have an architect/lead model subsystems and a general skeleton of the application, then have different teams implement the subsystems. Clearly defined interfaces on all inter-subsystem communications.