It would be a disservice to others with the disease and misleading to call it by another name and not include the common name. I don't mean you should be preachy or pedantic about it, but I don't think it is rude to say something like, "This is RA, which is different from osteoarthritis." Then if asked explain a bit more, but still briefly.
I am shocked that people are not aware of the difference, if only because of the ads. I only know one person with it, met one person who takes the shots and is a cyclist, one person who was being tested for it, and am related to a child with it (but never met her - first cousin twice removed).
I hope you can get it under control soon!