Crush is a body lust. It has more to do with how they look and behave then who they are. Nothing wrong with it but it is a bit superficial.
Love is one that you will get many opinions on but as I define it, it is a deeper concern for someone else's welfare that attaches your needs to theirs. It ties you in a way that keeps them from being miserable without there being some transfer.
Care is again more superficial and is closest to pity. You may pity a person who is suffering because of what you see them go through but you really don't know them well enough nor care enough to actually bind yourself to their fate.