Sleepy is wanting to sleep.
Being tired is wanting to rest, not sleep, just relax
After you eat a nice big meal, you feel sleepy, but if you do sleep, you only sleep for an hour or two, being tired is how you feel after a really hard days 12 or 16 hours of work, when you go to sleep that night you don't sleep for an hour.
Your brain (and body) go through a series of phases throughout the day in a rhythym that is to do with the timing of the sun. Your body wants to sleep (or is happy to sleep) at certain points of this cycle and at other points it wants to be awake. This is why sometimes you can be exhausted but can't get to sleep, because you have messed with your own biological rhythym. You can be tired because your body is trying to make you sleep, but you can also be tired because you have done too much exercise, or not eaten enough, or other reasons. So sometimes you are tired and sleepy, but they are not always together.
They are both the same as far as I can see. I suppose there is a difference between mental tiredness and physical tiredness. Sleep seems to be dominated by mental exhaustion rather than the physical. You can be physically exhausted but if your mind us racing then you won't sleep.
Whats the difference between being tired and feeling sleepy ?