These are all non-profits that work closely with a university and have basic research as a premise. They are both privately and publicly funded. I think that is different than a private corporation. Having worked in R&D at GM, and currently applying to jobs as I exit graduate school, the trend that I have seen personally as well as talking to many research scientists at private corporations is that R&D is an expense and must be focused on a business case. In discussion with some long term employees at some of the most research-motivated companies, this is in contrast to what private research was 20 years ago. Number of people, funding, and capabilities have been in decline. General Motors used to have an applied math research group and 10x more people in R&D! This led to things like the catalytic converter, the artificial heart valve and more. From what I have seen, nowadays private research will quickly test out a problem over the course of 6 months to maximum of a year, but will not do a 5-10 year project like academia has the freedom to do. These projects also like @gp stated, must have an application and not just be intellectually stimulating. Take it for what you will, this has just been my experience, but there are massively different purposes for current day private vs public research, which didn't use to be the case.