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The dreaded 15 point hand

It's a very basic question, but worthy of conversation in my mind.

You open. Partner responds. Now you have to limit your hand.

When talking about ranges of opener's and responder's hands, a maximum opener (19-21) only needs a minimum response (6-9) and vice versa to have the 25 points for game.  A medium opener should have game points when combined with a medium responder (or better, of course).

Learning bridge, I've often heard that a medium opening hand is 16-18 points, but is it exactly?

The bidding goes 1-1-1NT.

How many points do you have?  12-14?  12-15?  With a balanced hand, 1NT is often 15-17, so it's likely 12-14.  Obviously I'm not referencing weak 1NT openers.

You rebid your suit.  1-1-3.

How many points do you have?  16-18?  15-18?  Where does a 15 point hand fall in various bidding sequences?  Do you stretch a 2 rebid to 15 points? Do you include the 15 points with a 3 rebid?  Of course responder could still invite game either way, but I'm curious what I'm missing about this magical 15 point hand.

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