Is Shanghai social security card a company or a company?

If you have a Shanghai hukou, do it yourself. It's in the street office where your account is located.

If it is a foreign hukou, the personnel will give you a Shanghai social security card (medical insurance special edition) after adding Shanghai social security. This card has no photos. This card can only be handled by the company.

If you are registered in Shanghai, you can apply for a social security card after graduation.

The social security card of Shanghai hukou has nothing to do with whether the unit has paid social security, and there is no need to copy the social security card number to the unit or something.

After getting the Shanghai social security card, you can go to the street office window to get this medical record card and use it normally.

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