In principle I understand the distinction. Implicit memory is not consciously recollected but has an automatic character i.e. while I'm solving a task in math, I'm automatically using the concept of numbers and maybe even counting which I have stored in my memory. Explicit memory on the other hand is the conscious recollection of particular bits of memory, like explicitly counting up to ten or maybe remembering my birthday.
What I'm wondering is this: Isn't this distinction somewhat arbitrary? Even if I consciously use a certain piece of memory to solve a task, isn't it the case that I still don't know how I manage to access this particular memory? And is this even only about memory? To me it seems that everything can be stored in some way (how I breathe, my birthday and the range of things I do when taking a shower) and isn't that the only type of memory we have? Shouldn't the distinction then be about how we use the things we have memorized? I mean is there evidence that implicit memory is stored in a structurally different way than explicit memory? Or am I focussing on the wrong question?
I'm asking this question out of pure interest as a cognitive linguist who doesn't have much to do with memory right now.