Session Cookies: these cookies do not contain an expiration date - they are stored in memory as long a the respective browser session is running. When the browser is closed session cookies are lost.
Persistent Cookies: are stored to disk with an expiration date set - this means, that these cookies remain stored until the expiration date is reached or they are deleted manually. This type of cookies often is used to store individual user settings or to track user behavior for advertising reasons.
The domain attribute of a first-party Cookie will match the domain that is shown in the address bar of the web browser.
Third Party Cookies belong to a domain, obviously not shown in the browser-bar. This is the consequence of integrating external services into webpages - ie. advertising, analytics, statistics, cookie reminders ...