They have different ideologies behind them, but they refer to almost exactly the same class of software. A license that doesn't allow commercial use is proprietary and closed source.
Not closed source since the source is public and freely given [1].
Not open source because the license [2] forbids use based on field of endeavor which is required in the OSD [3].
As for the other direction, you can't have software be Open Source and closed source simultaneously since being Open Source requires the source to be available. Or in symbols.
According to most of people who invented the term "open source", the OSI and their open source definition, propritary software, even if you can see the source, is not "open source".
Nearly everyone uses the term "open source" this way, and to use it otherwise is grossly misleading.
Of course, if you follow the osi definition you are absolutely correct. [1]
"the obvious meaning for the expression “open source software”—and the one most people seem to think it means—is “You can look at the source code.”" [2]
The main problem imho lies in the fact that afaik we still don't know how to call proprietary software with released source code, although this is mighty common (again, see github). If that problem is solved, the osi definition is much better applicable.
(On a side note: A word that might describe such software is public. Public Software vs. Open Software Software. This however is again problematic because of "public-domain" software.)
> the obvious meaning for the expression “open source software”—and the one most people seem to think it means
I disagree. I think if you ask nearly people who know what the term "source code" means, if you ask them what "open source" means, they'll give the OSI definition (which is in practice the same as the FSF's 'free software' definition). They'll say it's more than "I can look at the source", but includes the rights to share and build on it.
Microsoft tried the term "Shared Source", which might be what you mean.