Sorry, this is not true. Free software simply means that the software grants the user 4 fundamental freedoms: the freedom to run, study, redistribute, and modify. It does not require virality, though it is encouraged.
From what I understand, Free Software and Open Source are largely similar, except that the former is political and moral, while the latter is mostly concerned about practical effects.
No, open source and free software are synonyms according to proponents of both terms, including Richard Stallman, the most prominent “free software” crusader. All (or at least virtually all) Free Software Foundation-approved licenses are also OSI-approved, and vice versa.
Your misconception is very common, but you, and other people with the same misconception, are conflating a few different things. Most of the people who prefer the term “free software” also prefer copyleft licenses to permissive licenses. Which is where the misunderstanding that “free software” means copyleft licenses and “open source” means permissive licenses comes from.
Yes, I'm viewing the concept of Free Software and Open Source through the political not legal lens. Sorry for that - I should have been more careful in a thread focusing on the legal parts.
Other than that I 100% agree either you.