Hello Fay,

A quick Google search brought up this for "Rheumatism":
Definition:

  1. [noun] any painful disorder of the joints or muscles or
connective tissues

  2. [noun] a chronic autoimmune disease with inflammation of the
joints and marked deformities; something (possibly a virus) triggers
an attack on the synovium by the immune system, which releases
cytokines that stimulate an inflammatory reaction that can lead to the
destruction of all components of the joint
     Synonyms: rheumatoid arthritis, atrophic arthritis
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In other words, the "Rheum" bit is in the blood.

and Arthritis is explained here:

The word 'arthritis' is Latin, from Greek 'arthro' (joint) and 'itis'
(inflammation). 'Arthritis' literally translates to "inflammation of
the joint".
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Sources:

http://www.appliedhealth.com/arthritis1.html

http://www.elook.org/dictionary/rheumatism.html

So your Doctor might think the pain in your thumb etc is muscular or
soft tissue damage and say your resulting pain is "rheumatism"

If your knee swells up is warm to touch around the joint he would say
that joint has "arthritis"

Of course this is just an internet answer and it's always best to ask
the doctor if you are unsure.

It seems to me I heard somewhere that SOandSO@webtv.net wrote in article
<12837-43418CDE-877@storefull-3256.bay.webtv.net>:

There are two major types of arthritis, rheumatoid arthritis and
osteoarthritis.  

Rheumatoid arthritis is a disease of the immune system, and can damage
both soft tissue and bone, especially around the joints.

Osteoarthritis is most a disease caused by wear and tear or injury which
eventually damages the joints including the cartilage which cushions
them.

Perhaps you're remembering the old time use of "rheumatism" for general
aches and paint, but the modern use of the word is much more precise.

The preferred specialist to diagnose and treat either variety of
arthritis and the many related diseases is a rheumatologist.