The difference between Persist and Remain

When used as verbs, persist means to go on stubbornly or resolutely, whereas remain means to stay behind while others withdraw.

Remain is also noun with the meaning: that which is left.

check bellow for the other definitions of Persist and Remain

Persist as a verb (intransitive):

To go on stubbornly or resolutely.
Persist as a verb (intransitive):

To repeat an utterance.
Persist as a verb (intransitive):

To continue to exist.
Persist as a verb (computing, transitive):

To cause to persist; make permanent.

Remain as a noun (mostly, in the plural):

That which is left; relic; remainder.
Remain as a noun (in the plural):

That which is left of a human being after the life is gone; relics; a dead body.
Remain as a noun:

Posthumous works or productions, especially literary works.
Remain as a noun (obsolete):

State of remaining; stay.

Remain as a verb:

To stay behind while others withdraw; to be left after others have been removed or destroyed; to be left after a number or quantity has been subtracted or cut off; to be left as not included or comprised.
Remain as a verb:

To continue unchanged in place, form, or condition, or undiminished in quantity; to abide; to stay; to endure; to last.

Examples:

"There was no food in the house, so I had to remain hungry."
Remain as a verb:

To await; to be left to.
Remain as a verb (copulative):

To continue in a state of being.

Examples:

"The light remained red for two full minutes."