Hello Léa Nicolleau,
I hope you are doing well

Same functionality. They're not two different features:
- Settings → Google Calendar setup = configures the OAuth connection (Client ID, Secret)
- Sync with Google button = triggers the sync using that connection

You set it up once via Settings, then the button lets you manually sync. A background cron also syncs  automatically after setup.
One is the configuration, the other is the trigger.

I hope this information helps you

Thanks & Regards,
Kunjan Patel