The biggest difference is the following: To RAISE is to do the action to something else, and to RISE is to do the action yourself.
In other words: You raise your hand. Your hand rises. You raise the price. The prices rises. The air conditioner raises the temperature. The temperature rises.
Here is the full explanation.
RAISE ? this word has many different meanings. Here are some common ones:
1) To move something to a higher position. (This is a rather formal use.)
Examples:
If you want to ask a question please raise your hand.
I couldn't raise my eyes from that book.
He started to raise his gun when the lights went off.
2) To increase something.
Examples:
They raised their price to $200.
The government intends to raise taxes.
Don't raise your voice!
3) To take care of a child.
Examples:
She has raised a wonderful son.
Lily was raised as a catholic.
His parents died when he was a baby and he was raised by his uncle.
RISE ? this word has many different meanings as well. Here are some common ones:
1) To move up. (This is a rather formal use.)
Examples:
We saw smoke rising from the house.
The plane is rising at two meters per second.
The rising sea levels may cause problems.
2) To increase, become higher.
Examples:
The price of oil is rising.
The fine will rise by 200% if you don't pay it on time.