The difference between these two is that the first relies on advertising while the second relies more on activities at the point of sale.
In a pushing promotional strategy, the firm takes the product to the customer. The firm does things like getting retail salespeople to push its product, perhaps by giving the retailer bonuses for selling more of the product. It creates displays in stores to get customers to notice its products. In other words, it is attempting to introduce the product to people once they are in the store.
In a pulling promotional strategy, the firm tries to get the customer to come to the product. This strategy tries to get customers to decide at home that they want a product and then to go to a store to buy that product. The most typical ways of doing this are through advertising and through putting specific items on sale.