different between aedileship vs edileship

English

aedile +? -ship

aedileship (plural aedileships)

(historical) The office of an aedile.
(historical) The period or duration of this office.
- 1845, Thomas Arnold, From the Gaulish invasion to the end of the First Punic War
  Two brothers of this name were, as we have seen, the authors of the law which threw open the offices of augur and pontifex to the commons, and afterwards in their aedileship they ornamented the city with several works of art

edileship (plural edileships)

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