Yes the intent of both tests is the same to check for microorganisms but Sterility Testing has a wider and deeper implication.
In Sterility Testing, the intent is to find if the batch is sterile / non sterile and only 2 liquid media - Trytic Soy Broth (for aerobic organisms) and Fluid Thioglycollate Broth (for anaerobic organisms) are employed and any growth in the media indicates that the batch could be contaminated and requiring further investigation. There is lot of considerations to be given for sample size too.
Bioburden test is to assess the load of the organisms in the articles and hence different solid agar are employed - each for bacteria, mold and yeast and different objectionable articles.
Incubation periods are different in both tests.
You could also take a look in the European Pharmacopoeia or the British Pharmacopoeia for more information.
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