Darrel's response answers most of your questions.
It seems to me it is all about emphasis. If I want to count fingers on a hand, I just count five. If I want to, for some reason emphasise the thumb is different, I call it a thumb.
Should I want to contrast the left with the right, I can do so. Otherwise, shuoulders. Be it on your shoulders how you use it.
I see that teether anf toother are both acceptable. <-- no clue whatthis means. Never heard of either, "teether" nor "toother".
We have a thumb, ...
I have recently been learning ....
Why? - That's English. All languages have historic remants, the way that was adopted. YOu can make up rules to cover most cases, or all cases, but in the end they simply describe what has been accepted as a convention for mutual understanding.