-itis means the part of the body is swollen, while -osis means the part of the body is damaged.
I found this out back in 2012, when I had a very nasty case of tendonitis in one of my feet, and I found out that the vast majority of cases of tendonitis should be called tendinosis instead, as it's pretty rare for the tendons themselves to swell; rather, the tendons themselves deteriorate from overuse.
swelling can happen without inflammaion, and mild inflammation may occur without noticable swelling.
-osis is a generic suffix for a process or condition: metamorphosis, scoliosis, hypnosis.
Calor, dolor, rubor, tumor
What if the part of the body is swollen and damaged?
Minor clarification, swelling does not necessarily always mean inflammation. -itis refers to inflammation of an organ or area of the both. Swelling, particularly when from fluid retention, is referred to as -edema. There is overlap though. :)
Does the suffix have any similar meaning outside of medicine? Like, osmosis?
-sis is just a noun-forming suffix.
Infection can cause an itis, but not all itis is due to infection. Such as inflammatory arthritis (noninfectious) vs septic arthritis (infectious).