Hi. You must be confused.
In my opinion,
sometimes, yes, they are the same meaning, also different meaning.
For instance, you got your feeling hurt, then you can use both.
“마음이 아프다”, “가슴이 아프다.”
And if you had indigestion because of eating too quickly or too much,
then you may feel your chest ache, in this case you should say
“가슴이 아프다”, not “마음이 아프다.”
To be brief, when it is related to physical situation, you say '가슴이 아프다'.
Normally, when we feel hurt, using both is natural.
Two more examples (only mental not physical)
I have a very important job interview this afternoon,
so I'm worried about it so that my heart is pounding.
both possible 마음이 두근거리다, 가슴이 두근거리다.
(only physical not mental)
I ran 100m as fast as I could, so I could listen to the sound of my heart beating.
you should say 가슴이 두근거리다. not 마음이 두근거리다.
I hope it is helpful for you.
Thanks so much for your kind explanation. It's so helpful to me. 고맙습니다. 선생님.