Why did ahab handle elijah differently from the way jezebel dealt with him?

Ahab followed in his father’s ways.He was a wicked king. He married Jezebel and submitted to her lead too.

1 Kings 16:31
And it came to pass, as if it had been a light thing for him to walk in the sins of Jeroboam the son of Nebat, that he took to wife Jezebel the daughter of Ethbaal king of the Zidonians, and went and served Baal, and worshipped him.

Elijah challenged Ahab to bring all of the Israeli people, including Baal's prophets to Mount Carmel. So, Ahab did as he was asked.

In front the multitudes, Elijah challenged the prophets of Baal to bring fire and rain, yet they failed to do so. Elijah then prayed to his God, the God of Abraham, Isaac, and Jacob, Yaweh to bring fire and rain. Yaweh brought fire and rain to the amazement of all but Elijah.

Elijah was feeling courageous until Jezebel found out what he had done to her prophets.She was furious and Elijah felt it was time to disappear again.

Basically, it's because of the fact that Elijah was not afraid to stand up to King Ahab, but when it came to Queen Jezebel, Elijah was scared, and it made all the difference in the way each treated Elijah. Ahab treated him decently, due to the fact he'd seen the miracles wrought by Elijah in the name of Yaweh and feared Elijah because of that.

Jezebel on the other hand, wasn't affected in anyway but anger by these miracles and deed done by Elijah in the name of Yaweh, and sought to kill Elijah. She realized that by seeking to kill him, he would be too scared to defy her.

In other words, it was because of how each one felt towards the miracles done by Elijah in the name of Yaweh. 

Hope this helps!

C.east asiais the answer.