In traditional form, it is 病徵 (sickness phenonmenon = symptoms of an illness) unfortunately, the simplified version is 征 which means "to conquer" or "to vanquish". 症 = disease. So 病症 literally means "sickness and diseases; hence all medical ailments to a living organism. I never trust anyone who says, "believe me".

there seems to be no radically differences between these words.believe me i'm a medical student in college.

My biological teacher said,病征 is a gather of a certain kinds of 病症.

''病征'' means symptoms of a disease and ''病症'' means illness. ------- yes.