Pretty good question Surreyfrog. I had to think about it for a while.
The way I view it is that a function - described by a use case - is something an actor would tend to do at one time. Say "book a ticket" in your cinema analogy. A process is something that has a number of activities / functions that tend to occur over a period of time. Something like process "See Movie at Cinema" which has activities like "View Whats On", "Book Ticket", "Drive to Cinema", "Park Car", "Collect Ticket", "Check Ticket", "Watch Movie", etc, etc.
Notice that some functions are manual and some are supported by a system. I recommend when you are modelling a business process to capture all functions in the process, including the manual functions.
Also notice that even this simple example has possible alternatives to include in the process like what if the Ticket is mailed or its an eTicket and you print it off before going. What if you pay when booking or pay when pick up the ticket. What if you walk to the cinema, etc, etc.
When you're modelling a process, what you thought initially was a simple function, when you look at it more closely, can turn out to be a process in its own right i.e. you may end up having nested processes.
Kimbo