different between frightfully vs rightfully

English

frightful +? -ly

frightfully (comparative more frightfully, superlative most frightfully)

From Middle English ryghtefully, equivalent to rightful +? -ly.

rightfully (comparative more rightfully, superlative most rightfully)

In accordance with what is right or just; fairly.
- 1859, John Stuart Mill, On Liberty
  The only purpose for which power can be rightfully exercised over any member of a civilized community, against his will, is to prevent harm to others. His own good, either physical or moral, is not sufficient warrant.
Rightly, correctly.
- 1590, Edmund Spenser, The Faerie Queene, II.viii:
  Ne euer will it breake, ne euer bend. / Wherefore Morddure it rightfully is hight.

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