, to laugh secretly, or so as not to be observed, especially while apparently preserving a grave or serious demeanor toward the person or persons laughed at.

To laugh out, to laugh in spite of some restraining influence; to laugh aloud.

To laugh out of the other corner (or side) of the mouth, to weep or cry; to feel regret, vexation, or disappointment after hilarity or exaltation. [Slang]

Source: Webster's Revised Unabridged Dictionary (1913)