JIK explained all this, but I'll do my wording nevertheless, because this stuff is very important to understand if you want to use tape.

Reel to reel should (and normally is) stored "tails out", which means you wind it before playing. It also means it is stored at a proper (and even) tension which doesn't damage it and that is why it is done that way.

Cassettes are a special case in that they're always ready to go. However, if they've been wound via the fast wind, they are often very uneven. In fact sometimes so uneven you can see it. To play these best, it is a good idea to play them once through without listening, and then play them for real after that. The reason is that when they are wound at the slow, guided, and even, pace of 1 7/8" things line up better and the tension is even. Doing it this way can sometimes avoid mechanical noises. For those who didn't get the idea from Joe, those mechanical noises are often coupled to the output because it vibrates the tape.

Regarding the suggestion of using a head demagnetize. That is not relevant to the discussion at hand, however you should not operate a tape recorder for very long before using one. Heads get slowly magnetized and you lose the high frequencies permanently if you don't demagnetize the heads.