(1) "Rise" means physically to get up, to ascend, to increase.
He rose from the chair.
The sun rises every morning.
The balloon had risen so high that it became difficult to breathe.
The price of oil had risen for many years, and then rapidly fell.
(2) "Arise" means to come into existence, to become noticeable, to originate from.
As the project continued, difficulties arose one after another.
The opportunity arose for him to declare his love for her.
"Arise" is old-fashioned in some ways. In poetry and the old language it sometimes means "rise": Arise, Sir Percival! In a biblical context concrete people may "arise": But false prophets arose among the people.
In modern ordinary speech, however, "arise" is usually limited to abstract subjects, as in my examples.
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