Third-party cookies are set by a domain other than the one you are visiting, usually by embedded services like ad networks, analytics tools, chat.
Strictly necessary cookies are the ones a website cannot function without: login sessions, shopping carts, security tokens, and load-balancing.
The ePrivacy Directive is the EU law that requires consent before storing or accessing information on a visitor's device, which is what makes cookie.
Prior consent means non-essential cookies and trackers must stay off until the visitor actively agrees. Consent given after scripts have already.