a pack slip denotes what should be "packed" for a delivery. It may consolidate several orders to a route, truck or customer.
a pick sheet denotes what items to pull from inventory. it too may be derived from consolidated orders.
for example:Customers A, B and C all have orders shipping today. Each customer is within 10min of each other and all will be delivered from the same truck/route. A single pack slip is generated, detailing the 3 customers orders (qty and items) for the truck.
depending on the type of picking utilized, one or several pick sheets may be generated. in this case, we'll say there are three "picking zones" in the warehouse. so three pick slips are generated, one for each zone. the pick slip tells each zone picker what items to pick. the three zones then deliver their picked items to a staging zone where the items are sorted into 3 boxes, one for each customer. these boxes get loaded onto the truck and each one is checked against the pack slip to ensure that each customer is receiving their order accurately.
in short: a pick slip facilitates the method/order/consolidation of picking items from inventory. a pack slip facilitates the method in which orders are consolidated/organized and shipped to a customer.
"pick" - pick it from inventory
"pack" - pack up the truck