What's the difference between having social security and not having social security in medical insurance?

Your family's medical insurance is nothing more than "new rural cooperative medical system" or "urban residents' medical insurance", both of which are just medical insurance, excluding pension. The social labor insurance (social security) purchased by the company is comprehensive, including multiple types of insurance, which is unmatched by your family.

As long as it is employed by the company, paying social security is mandatory by law, and you personally have no right to choose not to pay.

Contrary to what you said, you can stop paying for medical insurance at home. The medical insurance at home has social security, which is much larger than the scope and proportion of reimbursement at home, and the items not covered by medical insurance at home have social security.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.