das gleiche refers to
We both read the same (das gleiche) book (everyone has its own, but they look exactly the same)
while das selbe refers to
We both read the same book (one book, e.g. sharing, borrowing your book to your friend, the same object)
Does this differentiation exist in Spanish in contrast to English? I only found lo mismo, which is translated as das selbe/gleiche in my dictionary. Are there other adjectives that differ between the same object/same kind of object? Or what is the shortest way in Spanish to express this connotation?