Every Browser Has Its Own Cookies
Cookies are stored in the browser. Therefore, every browser has its own cookies.
When two different browsers visit the same web page, the cookies each has stored may be different.
How one browser can have different cookies than another browser
One browser may have visited web pages at the same domain that the second browser did not visit. Those web pages may have set or altered cookies in the visiting browser. Which would make the cookies in one browser different than cookies in the other.
The two browsers may have different cookie preferences. Which can result in different cookies in the two browsers.
The timing of when a browser loads a web page can affect the cookie's value. As can the type of browser. Either of those would make the cookie value given to browsers different than cookie values given to other browsers.
Because each browser keeps track only of its own cookies, two browsers on the same web page can have different cookies.
Will Bontrager