different between greatly vs profoundly

English

From Middle English gretly, gretely, gretliche, greteliche, equivalent to great +? -ly.

greatly (comparative greatlier or greater or more greatly, superlative greatliest or greatest or most greatly)

To a great extent or degree.
Synonyms: very, drastically
(archaic) Nobly; magnanimously.
- 1823, Catherine George Ward, The Cottage on the Cliff: A Sea-side Story (page 251)
  But all this our fisher, who was neither a poet, nor a dependent, did not know, so he concluded, that all who were truly great, were truly greatly minded, and noble in soul, as they were exalted by birth, and rich in splendour.

profound +? -ly

profoundly (comparative more profoundly, superlative most profoundly)

(manner) With depth, meaningfully.
He thought and wrote profoundly.
(evaluative) Very importantly.
More profoundly, it has shaken our most fundamental assumptions.
(degree) Deeply; very; strongly or forcefully.
From his childhood, she was profoundly troubled.

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