Gift this to the people whom you truly care.
Gift this to the people who you truly care.
The usage of whom and who both goes with the sentence? How do they make the sentence different?
Neither sentence is correct. Each needs 'for' or 'about' - we care for/about people. In my opinion, 'give' is more natural for most native speakers than 'gift'. It is certainly far more common.
Give this to the people for/about whom you truly care. Very formal.
Give this to the people who you truly care for/about. Less formal, but acceptable these days in all but the most formal of situations.
Give this to the people whom you truly care for/about. A mix of the formal and informal that is best avoided. "Because whom is unusual in an informal style, it is very rare in clauses that end with prepositions." Michael Swan (2005.452), Practical English Usage.