Strictly they are the same thing, as any medical dictionary will tell you. See the definitions on these pages:
http://medical-dictionary.thefreedictionary.com/nipple
http://medical-dictionary.thefreedictionary.com/mammary papi...

However, the nipple is strictly the mammary papilla; there are other structures in other parts of the body also called papilla. See here:
http://medical-dictionary.thefreedictionary.com/papilla

So although it is true that in context "a palpable tumor of the papilla", omitting "of the nipple", would have been understood to refer to the mammary papilla (nipple), it could in theory have referred to some other papilla; I presume the writer wanted to be absolutely precise and eliminate any possible ambiguity.

On the other hand, to have written simply "a palpable tumor of the nipple", omitting "papilla", would have produced a clumsy repetition of "nipple".

The words "nipple" and "papilla" are different in register; perhaps the writer was thinking of the former in organic terms, as it were, as a part of the body, and the latter simply as a physical structure.

Another factor might conceivably be that the writer wanted to make it quite clear (s)he was referring to the cylindrical protuberance properly called nipple or papilla, not to the surrounding circle called the areola; some people might understand the word "nipple" to mean the whole thing, though in medical terms the nipple is just the cylindrical protuberance.

So although it could be seen as a tautology, I don't think it's a mistake. It is a way of making the precise meaning absolutely clear.