Tapes are stored "tails in" or "tails out." One (the former, I think) means the tape is rewound so that it is as it was when new and unused--i.e., the tail of the tape is in the original plastic reel with the rest of the tape wound around it, ready to play from the beginning. If the tape is played or fast-forwarded to the end then the tail is out and the tape is wound around what had been the take-up reel on the right. "Tails out" is preferable for long-term storage, as I recall. The particular advantages I do not recall.
I think a safety tape is simply a backup copy made as insurance in case of the demise or loss of the original.
I think a safety tape is simply a backup copy made as insurance in case of the demise or loss of the original.