The definition of "Free Software" from the Free Software Foundation:
“Free software” is a matter of
liberty, not price. To understand the
concept, you should think of “free” as
in “free speech,” not as in “free
beer.”
Free software is a matter of the
users' freedom to run, copy,
distribute, study, change and improve
the software. More precisely, it means
that the program's users have the four
essential freedoms:
The freedom to run the program, for
any purpose (freedom 0).
The freedom
to study how the program works, and
change it to make it do what you wish
(freedom 1). Access to the source
code is a precondition for this.
The
freedom to redistribute copies so you
can help your neighbor (freedom 2).
The freedom to distribute copies of
your modified versions to others
(freedom 3). By doing this you can
give the whole community a chance to
benefit from your changes. Access to
the source code is a precondition for
this.
A program is free software if users
have all of these freedoms. Thus, you
should be free to redistribute copies,
either with or without modifications,
either gratis or charging a fee for
distribution, to anyone anywhere.
Being free to do these things means
(among other things) that you do not
have to ask or pay for permission to
do so.
The definition of "Open Source Software" from the Open Source Initiative:
Open source doesn't just mean access
to the source code. The distribution
terms of open-source software must
comply with the following criteria:
Free Redistribution The license shall not restrict any party from
selling or giving away the software as
a component of an aggregate software
distribution containing programs from
several different sources. The license
shall not require a royalty or other
fee for such sale.
Source Code The program must include source code, and must allow
distribution in source code as well as
compiled form. Where some form of a
product is not distributed with source
code, there must be a well-publicized
means of obtaining the source code for
no more than a reasonable reproduction
cost preferably, downloading via the
Internet without charge. The source
code must be the preferred form in
which a programmer would modify the
program. Deliberately obfuscated
source code is not allowed.
Intermediate forms such as the output
of a preprocessor or translator are
not allowed.
Derived Works The license must allow modifications and derived works,
and must allow them to be distributed
under the same terms as the license of
the original software.
Integrity of The Author's Source Code The license may restrict
source-code from being distributed in
modified form only if the license
allows the distribution of "patch
files" with the source code for the
purpose of modifying the program at
build time. The license must
explicitly permit distribution of
software built from modified source
code. The license may require derived
works to carry a different name or
version number from the original
software.
No Discrimination Against Persons or Groups The license must not
discriminate against any person or
group of persons.
No Discrimination Against Fields of Endeavor The license must not restrict
anyone from making use of the program
in a specific field of endeavor. For
example, it may not restrict the
program from being used in a business,
or from being used for genetic
research.
Distribution of License The rights attached to the program must apply to
all to whom the program is
redistributed without the need for
execution of an additional license by
those parties.
License Must Not Be Specific to a Product The rights attached to the
program must not depend on the
program's being part of a particular
software distribution. If the program
is extracted from that distribution
and used or distributed within the
terms of the program's license, all
parties to whom the program is
redistributed should have the same
rights as those that are granted in
conjunction with the original software
distribution.
License Must Not Restrict Other Software The license must not place
restrictions on other software that is
distributed along with the licensed
software. For example, the license
must not insist that all other
programs distributed on the same
medium must be open-source software.
License Must Be Technology-Neutral No provision of the license may be
predicated on any individual
technology or style of interface.
These definitions, although they derive from very different ideologies, are broadly compatible, and most Free Software is also Open Source Software and vice versa. I believe, however, that it is possible for this not to be the case: It is possible for software to be Open Source without being Free, or to be Free without being Open Source.
Questions
Is my belief correct? Is it possible for software to fall into one camp and not the other?
Does any such software actually exist? Please give examples.
Clarification
I've already accepted an answer now, but I seem to have confused a lot of people, so perhaps a clarification is in order. I was not asking about the difference between copyleft (or "viral", though I don't like that term) and non-copyleft ("permissive") licenses. Nor was I asking about your personal idiosyncratic definitions of "Free" and "Open". I was asking about "Free Software as defined by the FSF" and "Open Source Software as defined by the OSI". Are the two always the same? Is it possible to be one without being the other?
And the answer, it seems, is that it's impossible to be Free without being Open, but possible to be Open without being Free. Thank you everyone who actually answered the question.
