Show Used Cookies on Magento Website

No, they don't need to match.

The cookie domain defined, where the browser sends the cookies to:

• www.domain.com means the cookie is only sent to www.domain.com
• .domain.com sends the cookie to domain.com (I think) and every suddomain, so you can exchange informations between different subdomains/servers

The big issue is that Magento expects the website host name part of the URL to be what is listed in your BaseURLs.

So for example, if you have set Magento to serve out the site as www.example.com and someone comes in on example.com, Magento creates a session and a cookie for example.com, does a redirect to the BaseURL www.example.com and creates a new session.

The browser now has two cookies set and UX quickly goes downhill from there with cookie/session confusion shutting things down in weird ways.

Your best bet is to never let Magento get involved in this process. Use .htaccess rules or in your case, nginx rules to keep Magento in the dark and never see the non-BaseURL host name.

Set your cookie path/domain to match the choice made in your rules.

An added advantage also is that your customer "helpdesk" calls tend to go way down along with the misery of telling them how to delete cookies and history to attempt making the website function for them. Been there, done that, the teeshirt was no good and the experience no fun.