care?

     What does it mean when someone says they care about someone else?  There are an infinite number of ways to care about some one.  If two people live 3 states away, and there is never any face to face, phone, e-mail, snail mail, or any other contact between them, do they care about each other?  Seems like if one of the people is elderly and unable to initiate those forms of contact, then the other person could take the time to reach out and show that they care.  If the younger of the two people occasionally talks to other people in the family about the elderly person, does that mean that they care?  Seems that possibly they say that they care when really they are nosey and just wanting to give the impression that they care.  If they really cared, would they send a card?  When it was made known that the elderly person very much enjoys receiving snail mail but the younger person never once mailed a card or a picture of their young children, do they still care?  Aren't they just feeling guilty that they don't interact with the person?  
These are some common definitions of "CARE":

noun

1. 1. 

   the provision of what is necessary for the health, welfare, maintenance, and protection of someone or something.

   "the care of the elderly"
2. 2. 

   serious attention or consideration applied to doing something correctly or to avoid damage or risk.

   "he planned his departure with great care"

verb

1. 1. 

   feel concern or interest; attach importance to something.

   "they don't care about human life"
2. 2. 

   look after and provide for the needs of.

   "he has numerous animals to care for"

     In the provision of what is necessary, seems like sending a card in the mail would contribute to the health and welfare of a lonely Grandparent.  I guess if someone just feels concern or interest in
another person, they wouldn't need to take any action to express that feeling.  They could experience that feeling and not share it with the one they were concerned or interested in.    So according to the first verb definition of care, someone on the outside of a relationship may not be able to know that one person cares about another.  That is a personal experience of feeling and does not, by definition, require any action.  I imagine that it is potentially uncomfortable for a person to feel concern or interest in another person and not express it.  This discomfort may manifest as anger towards those who are actively expressing their feelings of concern through action.  It may manifest as guilt and gossip.
From now on, I will find a better word than care.  I want to do more than just care about people from afar.  I want to be involved in their life.  I don't want to sit back feeling concern or interest in someone and allow it to go unexpressed.