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The ancient and arcane art of typesetting and font design is an ancient art and likely was shaped (warped??) by long term exposure to lead fumes and whatever toxins were in the ink. The theft of some of those mystic terms by modern computer wizards is both evil and usually flawed.
That said, x-height is not a measurement, either absolute or relative, until you add some modifier (large, small, ...) and then is only a relative comparison to other aspects of the characters (usually baseline to a vaguely defined line marking the top of most majuscule letters). It is of no real absolute relation to the point size of a font.
Em, on the other hand, refers to a space normally equal to the width of a majuscule (captial, upper case, ...) M, though many fonts define their em space to a slightly different width, especially italic and various ornamental types.
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