Do you mean these two integrations/connectors:
These are supposed to be identical and the GSC under the SEO category is an oversight and will be removed in the next update.
Also, the "Google Search Connector" is based on scraping and doesn't offer these statistics so just need to make sure.
Which of your methods generated most clicks? Are you sure the settings are identical in terms of time interval etc? I just tried it and they produce the same numbers.