A session cookie for a website only exists whilst the user is reading or navigating the website. When the user closes their web browser these cookies are usually removed.
A persistent cookie for a website exists on a users computer until a future date. For example the cookie expiry date could be set as 1 year, and each time a website is accessed over this period the website could access the cookie.
A secure cookie can only be used via HTTPS. This ensures the cookie data is encrypted, reducing the expose to cookie theft via eavesdropping.
First-party cookies are cookies set with the same domain (or its subdomain) as your browser's address bar. Third-party cookies are cookies set with domains different from the one shown on the address bar. The web pages on the first domain may feature content from a third-party domain, e.g. an advert run by www.advertexample.com. Privacy setting options in most modern browsers allow you to block third-party tracking cookies.