Love is when you want to be with that person so much that it upsets you to not see them once in a day. You'd want to do everything with them, cherish them, admire them, correct them but never leave them.
Care is like, looking after that person or thing, wanting the best for them but if the necessity arises, you won't actually mid leaving them to their own devices. They are important, but they aren't the centre of your universe.