What's the difference between a DVCAM tape that is mini and a MiniDV tape?
Originally there was miniDV which is a standard consumer tape format (using ME tape) holding DV (at the time DV wasn't really a file format in it's own right).

Sony released a professional version of this called DVCAM with locked audio and which records at a shallower angle, running tape faster at the expense of running time, to reduce dropout.  

You could use either DVCAM tapes (now known as DVCAM-L) which as well as holding more tape for longer runtimes used higher quality MP tape, or you could record on miniDV tapes in either DV mode (to remain compatible with miniDV cameras) or in DVCAM mode to take advantage of the better format.  (The larger tape format uses the same width tape so the same head is used for either.) More recently DVCAM mini tapes have been available which use the better quality tape in the smaller package.

So DVCAM encompasses a file format, a recording format, the larger tape format and a marque of professional quality tape in the mini size tapes.  DVCAM mini and miniDV tapes are interchangable but they are branded towards their intended use and there is a general difference in quality/price between the two.

In your case regardless of the brands written on the actual tape you should probably use miniDV if it holds DV and DVCAM or DVCAM mini if it holds DVCAM.  If there is nothing recorded on the tape then it is suitable for either.