When people register/subscribe on my Console website, they are automatically subscribed to receive Newsletters. Does that mean they receive all the newsletters I send to my contacts?

When the clients use the Register form, they are registered as Prospects and the Newsletter Subscription option is automatically turned on in their Client Information section. That only means they agree to be sent newsletters by you, not that they will automatically receive all of them. Then, only when you create a newsletter, you actually choose whom to send it to. The contacts in the groups you don't select (in Communicate menu > Newsletters > Create newsletter > 'Options' step) will not receive the newsletter.