While some figures out there prominently stick to either ideology, most people hold a mixture of the three (or more?) approaches, or are just happy using free software or contributing to it, without thinking too much about its philosophy.
The terms themselves are used interchangeably by many people. "Open source" has become more common, partly because free software can mean software that is given free of charge. (the standard "free as in free speech" or "free as in free beer" distinction). Moreover, both the Free Software Foundation, and the people associated with the Open Source Institute are on friendly terms with each other and answer questions, give feedback, accept contributions, etc. from each other or from people that do not belong to either camp.
Like I said earlier, the fact that some licences would qualify as open-source and not as free software is usually a negligible fact. While some esoteric software has been released under custom licences that are open-source while not free software, most of the important software out there (and most software generally started by individuals) is free as well. [2]
[2] It is advisable not to use a custom licence anyhow, as this tends to confuse users and fellow developers. There are many common licences to choose from. Check the GNU licences list and the list of open source licences for such lists.