By default, invoices are sent to the client address. CORE does allow you to send invoices to a different client contact address. Each client in CORE can have an unlimited number of contacts linked to it. If you set any contact as the 'primary' contact of the client, invoices are addressed to this person instead of the client. To add a client contact, check Add Client Contacts for details.
To email invoices to a Billing Contact instead of the client, make sure to select the correct option from the Actions menu > Email on the Invoices screen. Check CORE Help Center for details.