Is there a difference in the closing process between companies that use perpetual and period inventories systems?

Depends on what they mean by a "difference." Closing consists of closing ALL revenues, ALL expenses, and dividends or drawing. From that point of view, there isn't any difference whatsoever.

There would be a difference in the specific accounts closed. But there's a difference in the specific accounts closed from company to company, regardless of the inventory issue. If this was a homework question, I'd consider it a trick question and wouldn't want to answer it. There is no difference in the "process" itself, no. But, if they are trying to get you to think of the differences in accounts used in these methods, then they should ask for specifically what they want and not call it the "process."