Master's degree in science is generally not free in US, CANADA, UK, OZ, NZ? (Tuition) I had the impression that in general, PhD programs are the only really "free" ones in higher education in those typically high cost English-speaking countries that they charge no tuition, pay you to do research, teach, do scut work etc., give stipend, maybe free housing.  On the other hand, masters degree program would charge big tuition, less assistantship opportunities, likely no stipend? Even in Science. Is that right?
In the US, PhD students typically have their tuition paid by the federal grant that also pays them a salary or waived by their universities. It is not exactly free, but it may be paid on your behalf. 

My understanding is that also typically any student paid on a grant as a graduate research assistant has their tuition paid. This covers master's and PhD students. I don't recall if this is my institution's policy or NSF's, but it is pretty common. 

These are both common situations, but neither is guaranteed. The vast majority PhD students in STEM have their tuition covered somehow and also get work as GRAs or TAs or have some sort of fellowship or stipend. There are lots of models. Universities don't want to take on a long-term (4-6+ years) commitment to get a PhD student through to their dissertation while running the risk they might have to leave or work an unrelated job to cover costs. Master's students are less commitment (2ish years), but there are opportunities for them, too. 

The vast majority of GRA seekers that cold email me looking for positions are master's students without a job looking to get their tuition covered and make a half-time salary. PhD students mostly don't have to do this because they get some sort of package when they are admitted.