Answer: “To care for another as I care for myself” is the level of concern and caring, while “love thy neighbor as thyself” is fulfillment. When I am at the level of the former, it is regarded as “bestowal for the sake of bestowal,” when I have nothing to give.
When we ascend the degrees of spiritual correction, then from a period of preparation, we transition to the period of fear (worry or concern) in which a person learns to care for the others. He can’t fulfill them yet and only worries about them. A space, a desire to care, gets created. Then, the degrees of love follow, and then it is already clear how to fulfill others.