I’m late getting into this, but I’m very suprised that this topic generated so much interest.
Here’s how you know if you’re a real engineer.  If you’ve ever worked on (that is, designed, tested, specified, whatever) something such that you’re absolutely certain that if you screwed it up, then;
a)people would die or,
b)It would cost more than you’ll ever hope to earn in your life to clean up the mess.
I don’t have a P.E. but I will claim the title under both above.  In some cases, my own life was involved in a).
[hey, this is the pit, grant me a little bravado]
Seriously, in my 25 years in the aerospace business I’ve never run across a case of somebody needing a PE, and I’ve often wondered how, in my line of work, one would ever be needed.  I have PE’s working for me, but I didn’t know they had the license until after they got on the job.  None of this should be construed as a criticism of licensure - I fully understand the reasons and support the concept.  I’d never try to pass myself off as a PE.
Why did I never get licensed?  Well, seriously, when I was in school the cost of the testing was worth a lot of pizza and beer money, so I just put it off.  If they passed a law saying I needed to be a PE to do what I do, I’d not grumble - I’d take the test or get another job.   I suspect it would be much harder for me now than it would’ve been when I was fresh out of school, though.
The only thing I’ve done that might have come close to needing a PE was helping a friend of a friend do some testing on a homebuilt airplane, for which he paid me a day’s salary.  Did I do wrong?
Anyway, as far as the “software engineer” title goes, I always chuckle under my breath when I hear it.  I do know real engineers (under my definition above) who work almost exclusively with software, but they’d never call themselves software engineers.  They’re flight controls engineers, crewstation engineers, weapons or mission equipment engineers who work on things that just happen to be controlled by software.