Emulation may refer either to jealousy and envy or to earnest zeal stirred by another’s example. In the first sense it is sinful rivalry; in the second, it describes an attempt to provoke earnestness or zeal.
In Galatians 5:20, “emulation” translates a word used negatively among the works of the flesh, meaning the stirring of jealousy or envy. In Romans 11:14, it describes Paul’s hope of provoking his fellow Israelites to zeal, a good and purposeful use.
The King James Version uses “emulation” where the Revised Version generally uses “jealousy.” The distinction depends on whether the result serves the flesh by exciting envy or serves the Spirit by encouraging earnestness.