Is Player A's Woodland Changeling a 7/7? Or something else? I'm not quite sure how this works...
It doesn't matter if they share more than one type, it's an on/off thing.
From Gatherer: 10/1/2009 Sharing multiple creature types doesn't give an additional bonus. Coat of Arms counts creatures, not creature types.
So the changeling will be a 6/6, and Player B's creatures will each get +1/+1 from sharing a type with the changeling
Coat of Arms doesn't count the total number of creature types shared, it counts the number of other creatures that share a type. A Changeling of any sort will get +X/+X from a Coat of Arms, where X is the number of other creatures on the battlefield that have a creature type (yes, it's possible to not have a creature type - Nameless Inversion, for example).
The Woodland Changeling is a 6/6. There are 4 other creature that share a type with it, so it gets +4/+4. It doesn't matter how many creature types are shared between the two creature, Coat of Arms only counts the number of creature that match the condition. So even though Chartooth Cougar amd the changeling are both Cats and Beasts, they each only get +1/+1 from the other.