What is the relationship between employment unemployment certificate and social security?

It doesn't matter much. The unemployment certificate proves your unemployment status. You can take it to a new unit for employment, employment registration, and pay insurance after completion. Therefore, you are required to apply for an unemployment certificate before paying social security, so that your social security payment period can be continuous.

If you apply for an unemployment certificate, you can get unemployment insurance money, and the state stipulates that you can get it for up to 24 months; Re-employment within 24 months, employment registration, no longer receive unemployment insurance. You can also enjoy preferential policies such as free job introduction, free job transfer training, and participation in vocational training, but you can't go to social security during the period.

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