A Personal Area Network is typically an ad hoc network, but the terms are not interchangeable.
PAN is differentiated by range, typically up to a few meters, although I've seen definitions describing up to 10 meters. It's intended to connect devices within a short distance of a user (hence the "personal"). One of those connected devices could link to an external network, to access the Internet, for example.
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An ad hoc network is one that is created as or when needed for a purpose by the devices, themselves, rather than connecting the devices via a network infrastructure, like a router.
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