Units entrusted third-party social security to be operated and payment on behalf of the same meaning?

"The unit entrusts the third party social security to be operated" means that the company or organization entrusts the management of social insurance to the third-party service provider, which will deal with the company's or organization's social insurance affairs, such as social insurance declaration, records, inquiries and so on. However, it does not mean that the third-party service organization will also pay the social insurance fees on behalf of the company or organization.

And "paying social security on behalf of the company or organization" means that the company or organization authorizes the third-party service provider to pay social insurance fees on its behalf, i.e., the third-party service provider pays social insurance fees to the relevant departments on behalf of the company or organization.

Thus, although the two concepts are somewhat related, their specific meanings are not exactly the same.