La respuesta a la pregunta del titulo de este post es No. Mucha gente cree que ambos terminos significan lo mismo, pero esto no es verdad. Les dejo unas palabras de un artículo del gran Richard Stallman donde explica las diferencias:
Nearly all open source software is free software; the two terms describe almost the same category of software. But they stand for views based on fundamentally different values. Open source is a development methodology; free software is a social movement. For the free software movement, free software is an ethical imperative, because only free software respects the users' freedom. By contrast, the philosophy of open source considers issues in terms of how to make software “better”—in a practical sense only. It says that non-free software is a suboptimal solution. For the free software movement, however, non-free software is a social problem, and moving to free software is the solution.
Free software. Open source. If it's the same software, does it matter which name you use? Yes, because different words convey different ideas. While a free program by any other name would give you the same freedom today, establishing freedom in a lasting way depends above all on teaching people to value freedom. If you want to help do this, it is essential to speak about “free software.”
We in the free software movement don't think of the open source camp as an enemy; the enemy is proprietary (non-free) software. But we want people to know we stand for freedom, so we do not accept being misidentified as open source supporters.