The Same Origin Policy isn't some uniform clean axiom: it's actually a set of specific rules and special cases fossilized into the modern Web. You can't define the Same Origin Policy with a small short description that correctly captures essential details: the special cases actually matter in practice.
The rules for cookies are the rules of JS, and they aren't even perfectly well defined and browser independent. Cookies are very weakly protected in the modern Web because of these fossilized rules, which must be accounted for in the design of secure Web identification:
- The degree of communication between subdomains allowed by cookies is extremely useful (one subdomain can set a cookie that is used by another) but also a potential source of confusion, as the browser will not send back a cookie with the name of the domain that set it.
- A cookie set on an http Webpage will be sent back on the same domain on an https Webpage, without indication of origin.
On the opposite, modern Web technologies that can store data (like localStorage and sessionStorage) on the browser store (together with the "cookie jar") are segregated strictly by origin with exact domain and URL scheme.
The inclusion of an image from another site doesn't have to be done with an object with specified dimensions (unlike the frame elements where the layout is specified by the frameset page or page hosting the iframe), so the layout depends on the dimensions of the loaded image; at least a Webpage can verify whether an image URL can be loaded, which can sometimes tell whether a user is logged on a Website for example.
The rules for loading scripts and style sheets are special; this is a hole in the policy that's useful for interfacing with other domain: a script loaded from the domain providing the service can set some variable to store the result of a computation. This very dirty way to do remote procedure calls is called "JSONP".
And then, there are side channels for measuring load time of ressources a page doesn't have the right to see or measure...