I prefer to use term "programmer" to describe to people who I am, rather than "software engineer" etc. And because programming is what I truly love to do.
Even though, in my resume I use Software Engineer/Developer of course, because "programming" does not bring you money.
Why so? To be honest, I think that we, the programmers, rarely make real things. Real developers make buildings, software developers do not make anything real rather than text on computer screens.
In its root the purpose of programming as a job was developing programs that would automate processes of real economics. E.g. to automate industries(manufacture lines) or maybe to optimize transportation logistics. Today's economics is post-industrial economics. Basically, the economics that focuses on control of human attention and selling this "control" to other actors. Computer technologies is a big part of it, but it is loosely connected to automation.
Only a limited number (a big number, but still limited) of people are capable to program. This is quite specific kind of mind. And only a small subset of programmers are capable to think in terms of programming and in terms of how to influence other people (the true value of post-industrial economics) at the same time. So, the ordinary programmer, to be honest, does not fit well in this system.
On the other hand there are a lot of people who can't program, and they loosely understand computer systems, but they are good at the art of spreading influence. These people are primary agents of post-industrial economics, and they are truly rule this system. They occupy high positions in companies and corporations, and they spread their way of thinking and ways of management to other minorities (including programmers).
We, the programmers, have to deal with this situation somehow if we want to have our part of the economic pie. Perhaps, through the trade-offs and compromises. But we have to admit that we are only minor cogs in this system. That is how it is in the current Economic Formation.
Looking for better jobs in companies that value pure programming would inevitably imply of looking for companies that don't perform well in the post-industrial economics.
The solution that I see is to do an ordinary "software engineering" job the way the rulers of the System want us to do it, and in the way we don't like to do it. At the same time we can working on the stuff that we love, and in the way we love to do it solely (or maybe with cooperation with other programmers). This is the best practical compromise that I can think of.