No they don't. They know an architect draws pictures of buildings. An engineer draws pictures of a bridge and hammers away at a calculator (actually the first thing most people think of with engineer is probably either boats or trains or Star Trek). A banker sits and acts like a total dick. What architects, engineers and bankers really do is a complete mystery to people.
When someone asks what you do and they do not have any domain specific knowledge, you say you write applications, you're a programmer. That's all they want to know, they don't care what the details of what you write are. They don't want to know the differences between languages. They don't want to know what a structured grammar is and why you care about it. Those are details of your job, that's not what they were asking.
"I'm a system administrator. I keep computers working." That is the maximum extent people want to know about what I do. They're being polite in asking, they don't really want to know details. And at the end of the day they still think that all I do is sit on my ass and look at a computer screen. Just like the way they visualize a programmer, and a banker and a ...
"I keep computers working" and "I write computer programs" are on opposite sides of a conceptual understanding chasm - most people have tried keeping computers working, even if they hated it and failed miserably, but most people haven't tried programming, and don't really know what the concept means.
I, for one, wish more people understood what programming "looks like", so that I could actually talk to people about what I do without them being completely confused. People can visualize what nearly every other profession does day-to-day, but what programmers do is a complete mystery to most people. I tell people that I'm a writer for a language with a very structured grammar, but that's only part of the story.