What's the difference between trierarch and trireme?

Trierarch

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Definition:

• (n.) The commander of a trireme.
• (n.) At Athens, one who (singly, or jointly with other citizens) had to fit out a trireme for the public service.

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Trireme

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Definition:

• (n.) An ancient galley or vessel with tree banks, or tiers, of oars.

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