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In fact, it is very tricky to distinguish between these two words. you may find them as logical interface and physical interface, and you may find them being used interchangeably. But, based on the language, port is a physical connection while interface can be considered as logical connections allowed on the physcial ports or the configuration or the SW that defines the logic of the port.
Port is a physical layer in OSI model
Interface is a Datalink layer in OSI model