If something is discernable, you can "discern" it — you can see it, smell it, taste it, or otherwise tell what it is.
Can you discern the difference between discernable and discernible? Well, other than the spelling, they're exactly the same. Use either word to describe something that can be sensed or picked up on. If it's not discernable, then you can't make it out or tell what it is. A really good forged signature might not be discernable from the real thing, but there are plenty of discernable reasons why you shouldn't go around faking other people's autographs.