Is there any difference between the Blockcerts Universal Verifier at blockcerts.org and the implementation of cert-verifier(python) in the repository?
Yes,
Blockcerts Verifier is a UI around the cert-verifier-js code, which currently only verifies v2 and v3 versions of blockcerts.
There is another js verification library: @blockcerts/cert-verifier-js-v1-legacy - npm, which only does v1 verification and is not maintained.
To the best of my knowledge, the python verifier only verifies v1 certs too, and has not been maintained in years and there is no plan to evolve it on our side.
If you want server side verification, cert-verifier-js is node ready.