In basketball and lacrosse, the offensive player setting the pick must remain stationary at the moment of contact with the defender, and allow the defensive player a "reasonable opportunity" to avoid the screen; a screen is illegal if the screener moves in order to make contact, and obtains an advantage; the result is an offensive foul in basketball and a technical foul in lacrosse. There must be illegal contact for a moving screen to be a foul; no illegal contact, no foul, no matter how much moving the screener does. If the screener holds, leans or moves into the defender to cause contact, this will result in a foul on the screener.
In team sports like basketball and lacrosse, there's a rule against screens if the player setting it moves into the defender, giving them an unfair chance to make contact; this can result in a foul on either side, depending on the situation.