While this is not likely the show you describe, I thought I'd mention it anyway since it may be based on your show, or it may spark someone else's recollection, or something helpful. This is a short story called "Clothes Make the Man" by Neal Shusterman, I found it in Mindstorms: Stories to Blow Your Mind.
In the short story, there is a mixup between two kid's luggage while traveling - each picked up the wrong suitcase. As the protagonist kid ended up using the contents of the luggage (having nothing else, mostly), he found himself adapting to it
he fits the clothing - including growing a third arm, he develops an appetite for the alien food (a can of worms) while loosing interest in regular food, and I think picking up alien language.
The story indeed ends with the other kid's family showing up to swap the kids so both could be accepted (since the other kid had likewise adapted to this kid's items). The story ends with everyone pretty happy, and the kid's new parents teaching him to read their language.
The matching elements are the kids being swapped, looking like each other's people, and a happy-ish ending. The backstory (why they look different) doesn't seem quite the same, and the specific differences between the people's appearances is also different. Also, obviously, the difference between a show and a short story is also relevant, and the timeline is off (1996).
But while it may not be what you're looking for, I thought it might be related, it may spark someone else's memory, it may be someone saw your title but was looking for this work, so I thought I'd offer.