The difference between free software and open software can best be compared to a religious schism.

Both have a group of supporters behind them, both share some kind of dogma (freely distributable software for which sources are available and which you can use, modify and pass on).

The older, orthodox group is the one behind free software. The head priest of this movement is (without a trace of doubt) Richard M. Stallman, a genius hacker - the writeups about him will tell you more.

The Free Software folks church would be the Free Software Foundation.

A very dogmatic crowd, which would rather die than using a pacemaker running non-free software.

This approach makes the Open Source approach rather unpopular with commercial ventures.

On the other hand, we have open software. Open software is just like free software. With a minor difference in dogma, which we will cover later.
The head priest of the Open Software group would most likely be Eric S. Raymond (ESR), while another likely candidate (at least in the rank of a cardinal) would be Linus Torvalds.
Of course, there is a things similar to the FSF. The Open Software Foundation ?
'fraid not !
As this name was taken, the Open Software people settled on "Open Source Initiative". (Not to be confused with ISO-OSI, if course.)
Less dogmatic (let's say "More connected to reality the way we know it"), the Open Software groups has no problems to say that (even if Open Software is better than the prorietary stuff,) it is perfectly OK to use (and god beware, sometimes even write) proprietary software if no open alternative is available.
The main point for them is "Solve the user's problems".

To summarize:
Free Software -> orthodox
Open Software -> reform

Of course, the Open approach is much more acceptable to the commercial world.