That's a pretty simple distinction, but you've asked for us to define abstract concepts without using definitions or abstract concepts. So let's just say, knowledge is what you know and beliefs are what you believe. A belief implies some level of doubt, while knowledge is just the information you have in your head. There is a lot of overlap. I know that the sun will rise tomorrow, because I understand how the earth rotates and orbits the sun. I believe it will happen because I understand physics and observable phenomena. Put it another way, it is a high-confidence belief based on the knowledge obtained through observation and study. Some beliefs are based on nothing more than hope, and some knowledge is beyond any doubt. I believe the Phillies can win the World Series, but I know our bullpen pitches cantaloupes and our hitters are streaky as shit.