"To appreciate the difference" means to recognize and understand the distinctions or variations between things. It implies acknowledging the uniqueness of each item or situation and valuing those distinctions. Full definition
Many new writers don't fully appreciate the difference between copy editing and line editing, let alone the effect an editor can have on a book's success. (writerfulbooks.com)
To me, this picture book emphasizes that it's always best to be yourself and to appreciate the differences in other people. (uniqueteachingresources.com)
I didn't appreciate the difference until I slept on these sheets. (theinspiredroom.net)