(CNN) -

They call themselves "the resistance."

Israel and the United States call them terrorists.

What's unclear is who's calling the shots within the Palestinian militant group Hamas.

The political and the military arms of Hamas appear to have contrasting mission statements -- a push-and-pull that became apparent after Israel agreed to an Egyptian-proposed cease-fire in Gaza.

Mousa Abumarzook, a senior Hamas member, said the group was still "discussing" how to respond and "there is no official position yet from the movement on the Egyptian inititive."

But the military wing, the Qassam Brigades, didn't mince words.

"We in the Al-Qassam Brigades reject altogether the proposal, which for us is not worth the ink that it was written with."

So who's in control?

Analysts say it's hard to pin down precisely who has the final word on making decisions and guiding strategy.

"It's very much believed that the political wing, the political leadership inside Gaza and externally, was counseling for restraint," said Neri Zilber of the Washington Institute for Near East Policy. "The military wing very much had other ideas,"

Here's an introduction to Hamas' key players:

THE POLITICAL WING

KHALED MESHAAL

He's Hamas' top political leader and often its public face. He's had the role since 2004 after Hamas' then-leader, Abdel Aziz al-Rantissi, was killed in an Israeli airstrike.

A former teacher, Meshaal operates mostly from Qatar and is known as Hamas's external deal-maker, raising money from supporters in the region.

"Despite his George Clooney-type looks, he's very much a dangerous man because he aids and abets Hamas' very destructive policies and strategy," Zilber said.

A bizarre assassination plot: In 1997, Meshaal was the target of a bizarre assassination attempt by the Mossad, Israel's intelligence service.

Mossad's agents confronted Meshaal in Jordan and injected poison into his ear.

It might have ended right there. But Jordan's King Hussein, who had a peace treaty with Israel, threatened to break off relations unless Mossad delivered the antidote to the poison. And they did.

"Allah saved me. Then King Hussein," Meshaal told CNN in 2002.