“First party” and “third party” describe who is interacting with you in the current site context, not whether the tracking is good or bad.

If you visit example.com:

• storage/scripts operated by example.com in that context are first-party;
• resources from another domain — advertising, analytics, embedded widgets, etc. — are third-party.

Historically, third-party cookies made cross-site tracking straightforward: the same advertising domain embedded on thousands of sites could recognize the same browser. Modern browsers increasingly block or partition third-party cookies/storage, reducing that particular technique.

But “third-party cookies blocked” does not mean “not tracked.” Sites and ad systems can still use:

• first-party identifiers and server-side data;
• logins and email/account linkage;
• URL parameters and link decoration;
• browser/device fingerprinting;
• IP/network information;
• data shared between companies outside the browser.

Likewise, first-party data can persist between visits even when you are logged out. A site can store cookies/local storage under its own domain or associate behavior with other identifiers.

Takeaway: Blocking third-party cookies closes one important tracking channel. It does not make the browser anonymous or stop the site you are visiting from remembering you.