difference between large signal s parameter and x- parameter

S-parameters are Port parameters and they are linear.They don't have any information about nonlinearity about the device.
X-Parameters behavioural parameters and they are nonlinear and they have nonlinearity information about the device.

LARGE signal s-parameter is not have non linear information?

No,large signal s-parameters are always linear.The difference between small signal s-parameters is signal drive level only.They corralate port realations such as reflection,transmission,isolation.