Similarity: Involved employing supporters to office
Henry Clay supported John Quincy Adams during the 1824 election; in return, John Quincy Adams made Henry Clay Secretary of State after defeating Andrew Jackson for the presidency.
During his presidency, Andrew Jackson gave office jobs exclusively to his democratic supporters.
Difference: Not much difference, but the Corrupt Bargain happened during and after an election while the spoils system was developed during Jackson's presidency.
