Is there a type of arthritis that only effects the tendons? if so what's it called? how is it diagnosed and does it always shows up on mri?

Tendinopathy: Arthritis by definition is a disease of the bones and not the tendons. There are conditions where only the tendon can be involved and not the joints (tendinopathy). It does not always show up an an mri. Newer mri's (3t) may be better at detecting it. Depending on wehre the tendon is, musculoskeltal ultrasound can be better than an MRI is picking up tendentious conditions.

No: Osteoathritis can irritate periarticular tendons, but osteoarthritis doesn't target tendons directly. Rheumatoid arthritis or other rheumatologic diseases can affect insertions sites of tendons, called enthesopathies. However, the primary target of rheumatoid arthritis is the synovium (lining of joints). Tendons also have a synovial lining and that's why they are affected.