When server A sets a cookie for server B, the server B cookie is a "3rd party cookie". Whether server B is on a different domain than server A determines if the cookie is a "cross-domain 3rd party cookie" or not.
Don't think of "3rd party" in the same way as you think of 3rd party software and don't associate "3rd party" with a web site's ad affiliates.
3rd party cookies by design are not bad and many sites legitimately use them. Hotmail for example, is one site that requires that cross-domain 3rd party cookies be allowed.
A 3rd party cookie does not have to be an evil cookie from an ad site like doublelick.net or sneaky sites.
A 3rd party cookie is just a cross-server cookie.
(As far as this explanation of Opera's cookie settings are concerned.)
The setting "Accept all" for normal cookies is labeled incorrectly and does not reflect what actually happens when you select that option. It should be labeled "Accept only cookies not blocked in server manager" as that's what that setting does.
I burnout426 can confirm this. Even if "Normal cookies" is set to "Accept All", Opera won't allow domains or servers to set cookies if there's an entry for the domain or server in the server manager and its properties are not set to allow cookies. This means that you can indeed accept all cookies and blacklist certain domains/servers.
For example, if you wanted to "accept all" normal cookies, but block all servers from domain.tld, you'd enter domain.tld in the server manager and in its properties, you'd check *only* "apply these settings for entire domain". For a server, you'd just make sure no boxes are checked.
The 3rd party setting "Refuse all cookies"is labeled incorrectly and does not reflect what actually happens when you select that option. It should be labeled "accept for the current domain only" as that's what that setting does.
The following explanation will be based on the current, default labels for Opera 8.
Normal cookies: Refuse all
All cookies are turned off. (even 3rd party)
Normal cookies: let me decide every time I receive one
Each time a server tries to set a cookie, Opera will ask if you want to allow it. Whether Opera automatically accepts, denies or asks you about 3rd party cookies depends on the global 3rd party cookie setting.
Normal cookies: Treat as specified in the server manager
Turns off regular cookie handling and use the server manager instead. The server manager acts like a white list of servers that you want to allow the acceptance of cookies for. For 3rd party cookies, for one server to set a cookie for another server, both servers must be entered in the server manager and set to allow normal cookies. Then, whether or not 3rd party cookies are allowed for those servers depends on the global 3rd party cookie setting.
Normal cookies: Accept all
This is a misnomer, because it "Allows" the acceptance of all cookies except those blocked in the server manager. Whether 3rd party cookies can be accepted or not depends on the 3rd party cookie settings.
3rd party cookies: accept only cookies set to the server itself
Refuses all types of 3rd party cookies no matter what the normal cookies setting is.
3rd party cookies: Refuse all
This is the other one that is labeled incorrectly. This one allows 3rd party cookies, but not across domains. For one server to set a cookie for another server, they both have to be on the same domain and both be allowed by the normal cookies setting to set normal cookies.
3rd party cookies: let me decide every time I receive one
Just like the corresponding normal cookie setting. If you choose to allow a server to set a cookie for another server, both servers need to be allowed (via the normal cookies setting) to set normal cookies.
3rd party cookies: accept all cookies
This allows the acceptance of all types of 3rd party cookies. Again, for a server to set a cookie for another server, they both must first be allowed (via the normal cookie setting) to set normal cookies.
Normal cookies: Treat as specified in the server manager
3rd party cookies: Accept all
What that means is, refuse all types of cookies for all servers, except for servers that are set in the server manager to allow cookies.
That is equal to turning off cookies in Firefox and using the exception list.
Now, if you know for sure that you don't visit and sites that require "cross-domain" 3rd party cookies, you can set the 3rd party cookies setting to the incorrectly labeled "Refuse all". (Remember, "Refuse all" doesn't actually refuse all. It just blocks cross-domain cookies.)
Now, if you know for sure that you don't visit any sites that require any type of 3rd party cookie, then you can refuse all 3rd party cookies by setting the 3rd party cookies setting to "Accept only cookies set to the server itself".
There are normal entries and dynamic entries.
Here is an example of a domain in the server manager:
For yahoo webmail, there are certain servers that need to set cookies. Put simply, it's just easier to accept cookies for the entire domain and then Opera will dynamically add the specific yahoo servers needed to log in.
Example of dynamic server entry for yahoo.com
As far as Opera is concerned, site.com is a domain and www.site.com is a server. If you want to allow cookies for the entire domain, make sure you use site.com and not www.site.com because www.site.com is not a domain.
Now, if you know the site only requires one server for cookie purposes, you can add just that server instead of the entire domain.
Example of server in server manager
Note: The reason for "ignore this option" for a setting means that I could not find that it actually does anything.
This page's explanation uses a different meaning for a "3rd party cookie" than the correct meaning. This is to make Opera's settings make sense.
However, here is a Cookie Settings table with meanings taken from Opera's opera6.ini knowledge base. This would be the official meanings for the settings, which are based on the correct meaning of a "3rd party cookie".
Now, here is a different table that tries to explain Opera's cookie settings in a more specific manner, while following the correct meaning of a "3rd party cookie".
Since Opera's cookies settings are not necessarily worded correctly, use whatever explanation of the settings that helps you understand so you can configure Opera to produce the results that you want.