Jizya was for Non Muslims and Zakat for the Muslims
Thats the difference, and both went to help the populous itself.
The Jizya is a tax levied on non-Muslims in lieu of military service which is compulsory for Muslims but not for non-Muslims.

The amount of Jizya is much less than the Zakat, which is levied on Muslims only. The non-Muslims paying Jizya were exempt from compulsory military service (and were also entitled to many rebates in this regard) in a Muslim State but were entitled to full protection.

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