What are other religions' equivalents to Priests?

This is tougher than you suppose! For example, Christianity has priests, ministers, and pastors, depending on the denomination, but, they are not exactly equivalent.

Priests preserve the "sacerdotal" or sacrificing element of the original Jewish Levite priests. These were the people who make the sacrifices at the Temple for Jews who wished to atone for their sins. Christian priests no longer do actual sacrifices, but, hold an "anamnesis" or memorial of Christ's sacrifice. So, the Orthodox, Catholics, Anglicans, Lutherans, and some others have priests, as they link their role with Christ's sacrifice, namely in doing the Mass/Holy Communion/Eucharist/Last Supper.

Other denominations, notably Protestants, have pastors, as they act like a shepherd herding the flock. Some are called ministers, because the minister to their congregations. Most Protestant denominations have ministers/pastors.

Jews have rabbis, which literally means "teacher."

Muslims have immans. Mullahs are religious experts.

Hindus have priests.

Shintos priests. Well, in English. I do not know the Japanese word.

I forget what Sikhs have. We have a multi-faith religious panel that tours our town once a year, but, i can't remember the title the Sikh went by! A very nice man though, if that helps.

The usual equivalent is priest, but, that is mostly a translation to English. I doubt that many (if any) of them have a sacerdotal role. The "default setting" for religious leader in English is priest.

Our Jewish friends call them a Rabbi

Our Protestant friends call them a Pastor

Vicar, Reverend, Brother are other terms used by various groups.

Christianity = Bishops

Jewish = Rabbis