I don't understand the difference between 'connection link' and 'presential link' in the configuration of the emails

The login link is the access link to your web page and your live show. It is to be sent to all your participants who watch the live remotely.

If several of your participants are in the same place (in a meeting room or on site if your live event is hybrid), you can send them the in-person link so that they can open it from their phone and take part in the activities.