"I promise that I care" conveys a commitment to caring for the other person, suggesting that their feelings are genuine and heartfelt.
"Much more than I show" acknowledges that the speaker may not always fully convey the depth of their care through their actions or words. It recognizes that sometimes emotions are not readily visible or expressed.
In essence, this statement is an acknowledgment of the speaker's intention to assure the other person that their feelings and care are genuine and profound, even if they may not always be readily apparent. It highlights the complexity of emotions and the importance of communication in expressing one's feelings.