Are (Shenzhen Labor and Social Security Bureau) and (Shenzhen Social Insurance Fund Administration Bureau) the same department?

There is no Shenzhen Labor and Social Security Bureau. After institutional reform, it was renamed Shenzhen Human Resources and Social Security Bureau.

Shenzhen Social Insurance Fund Administration is a public institution directly under Shenzhen Human Resources and Social Security Bureau. Not a department, the former is a subordinate unit of the latter, that is to say, Shenzhen Human Resources and Social Security Bureau is the competent unit of Shenzhen Social Security Fund Administration.