What is the (subtle) difference between the three ways to typeset unnumbered equations (if any)?

The first is the plain tex,

$$ E = mc^2 $$

The second is the LaTeX

\[ E = mc^2 \]

And the third is the AMS,

  E = mc^2

As far as I can tell, the end results are almost the same. If there's any difference, most likely in the spacing around the formulas. But I cannot find any concrete reference for the later two.

  • With \usepackage{amsmath}, methods 2 and 3 are exactly the same. – egreg Jun 20 '16 at 9:50

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