Tendonosis is generally chronic, as-in not acute but just annoying. I've had mine for about a year and have kept playing relatively regularly. I've reduced it by about 75% from where it was initially through daily stretching and being careful.
Tendonosis usually doesn't affect you too much while playing - it might play up near the end of a hit etc but generally you can function. It's afterwards - often hours later or the next morning especially when you notice it. My Achilles isn't aching sore but is mildly tender to squeeze between by thumb and forefinger.
If you had tendonitis playing tennis would almost certainly get more and more painful.
treatment usually allows for light activity (e.g. non-serious tennis, light running) with stretching and sometimes medical treatments. Icing/compression tend not to help much at all.
treatment is usually immediate stuff like rest, ice, compression etc and laying off the activities completely. Then a gradual build up back into activity.
A couple of links which you might find interesting as part of learning more:
A good thread on this site: http://tt.tennis-warehouse.com/showt...ight=achillies
One of the best related stretches you can do. I do this twice daily and credit it with much of the success I've had with alleviating my issues: http://www.youtube.com/watch?v=DgHoe...eature=related
A general info site on the various types/causes/levels etc: http://www.achillestendon.com/Injuries.html