I can do 'em all. Big laugh, small laugh, chuckle, exhale air from nostrils, maniacal, petty, mocking, robotic, snicker, high-pitched, low-pitched, sarcastic, bombastic, slow, astonished...I've done a bit of cry laughter, in my time.
Cry laughter is a mix of "I can't believe this happened, and it hurts, but it's also absolutely hilarious." Rarely used, but it comes natural when a football hits where the sun don't shine.