I am not primarily a MSK physio so someone else with more knowledge might give a better opinion.
My understanding is that impingement is a syndrome and bursitis and suprspinatus tendinopathy, partial or full tears are specific conditions. Impingement syndrome is an overarching term that involves a huge number of pathologies and potential aetiologies. Impingement syndrome would include all these conditions plus conditions involving other tendons etc. There are a huge array of tests that people claim can differentiate one from another. I have attached a recent systematic review of the accuracy of these tests. This will help you choose the best tests to use. If you find a test in the review that you don't know there are lots of visual references on the net and on Youtube on how to perform the test - just try to use a reputable source. Otherwise the book below is great.
However clinical tests are limited in what they can diagnose and identifying a test that differentiates solely one pathology in the shoulder is difficult to do. On the whole many tests tend to be sensitive (the proportion of actual positives which are correctly identified) and fail to be very specific (the proportion of actual negatives which are correctly identified).
So if someone says they have the perfect test that differentiates bursitis from tendonopathy I would take that with a grain of salt.
Don't forget how important the patient's history is; this may give clues to the onset, development and presentation of a specific pathology.
Here is a nice background paper on diagnosis and management but not very evidence-based:
Shoulder Impingement Syndrome: eMedicine Sports Medicine
I have found Robert Donatelli's book: Physical Therapy of the Shoulder is a great book for all aspects of physiotherapy for the shoulder:
Amazon.com: Physical Therapy of the Shoulder (Clinics in Physical Therapy) (9780443066146): Robert Donatelli: Books