'Posture', used as a noun, means the way a person sits, stands, the way they hold their head and shoulders. A posture may tell something about they way a person feels, but it may not be intentional.
"His posture indicated that he was angry."
"She had a relaxed posture, arms at her sides, with a serene expression on her face."
'Gesture' as a noun means some movement by a person to intentionally convey some message. Waving to a person is a gesture of friendship. Shrugging you shoulders is a gesture meaning that a person doesn't know something.
"He gestured at Tom with his hand, indicated that Tom should come over."
"She gestured with a wave of her hand that they should leave her alone."
In short, a posture can be intentional or unintentional, a gesture is always intentional.