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This is a topic that I've had come up a number of times. I find the best way to get some people to think of the difference is to use common examples. Android is what I normally point to as an example of open source with which almost everyone is familiar, and most have used. It also give you an easy example of how different device manufacturers make use of the open source Android OS. I would use Linux, but if they know what Linux even is, they usually understand the difference.
Here's an article that discusses directly the differences between freeware and open source...
"Freeware refers to software that is, well, free of cost to use for an unlimited period of time...Freeware may be proprietary in nature, in that the source code may be closed to users, but not necessarily.
"Open source software refers to software whose code is open to users to use, change and improve the product, as well as to redistribute the modified forms."