Free software foundation was first introduced in 1985 by GNU founder Richard Stallman. Stallman believed that software beyond the monetary sense should be free to run, share, and modify.
Open source software movement came about by a gentlemen named Eric Raymond. Raymond believed that the free software movement needed to appeal to more commercial entities. Thus, Raymond founded the OSI - Open Source Initiative which introduced and encouraged the option of sharing software and modifying through the use of licenses. This ended up creating a platform in the marketplace for free software with a twist in comparison to the free software movement where true enthusiast of the movement believed it should be open and free without any restrictions to the end user.
Although the free software and open source movement are similar in the sense that they push for free software. The most important differences is that open source creates a platform for free software in the market place through the use of licenses and communal projects.