If a contact unsubscribes from autoresponders, does that mean s/he is also unsubscribed from newsletters and vice versa?

No, not necessarily. If a contact unsubscribes from one communication service, the system will not also unsubscribe her/him automatically from the others. Subscriptions to newsletters and autoresponders are two separate features.

Contacts can unsubscribe themselves from any autoresponder and all other communications sent from your Console, using the unsubscribe link in the footer of the communications, that sends them to the dedicated "Unsubscribe" page, where they can choose and save their options. You can test this yourself with a test client, configured just like any other contact in your CONTACTS tab.