What's the difference between elogist and eulogist?

Elogist

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Definition:

• (n.) One who pronounces an eloge.

Example Sentences:

Eulogist

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Definition:

• (n.) One who eulogizes or praises; panegyrist; encomiast.

Example Sentences:

• (1) Commentaries on Ferguson were universally eulogistic.
• (2) Putin may be preening himself on his cunning opportunism in upstaging Obama, and on his eulogistic coverage in the west.