In this context, collections and receipts have the same meaning and are interchangeable.
As for who receives the monies, that is based on a sliding scale. The percentage that goes to theater owner and distributor changes depending on how long a movie stays at a theater. The longer a theater shows a film, the greater the percentage of the ticket price goes to the theater.
The theater takes in a small percentage of the ticket price initially, but each week gains a larger percentage of the price. The percentage that doesn't go to the theater is given to the distributor.
As for the distributor and producers, their contract is based off of the non-theater take of collections/receipts and is independently negotiated. (Keep in mind, that some producers are the distributors, some independently finance, and some collaborate.)