John Conde's answer, which is currently voted #1, is wrong because of an overly pedantic emphasis on PageRank, which is both a) a formula which is detailed in a publicly accessible research paper and b) Internet shorthand for "the sum of all algorithms Google uses to rank pages", which is a far wider topic than PageRank proper.

In the sense intended by a question, there is absolutely a difference in Google's treatment of two pages based on whether they are on the same domain or on two subdomains of that domain.

One factor is what SEOs call "domain authority" or "domain trust." A link to any page on a domain says that the linked page is authoritative for the linked topic (the one mentioned in anchor text), and the linked page is authoritative for other topics, and that the linked domain is authoritative for other topics. This is beyond question: it is why Wikipedia ranks for more queries than God, despite not having huge numbers of in-links to newly created articles. It is why a popular blogger is more likely to rank for a newly created article (with no links) than an unknown blogger, even if their title and other on-page factors are identical.

In general, Google is thought to treat subdomains as having a lesser relationship than pages within a domain: they do not fully share domain authority amongst each other. This solves problems like the technique, prevalent a few years ago, where folks would use a profusion of automatically generated subdomains (chicago.example.com, boston.example.com, 67k examples elided, etc) to achieve higher rankings.

This is one of the major reasons why SEOs advise clients to put blogs on example.com/blog rather than blog.example.com .

There are also issues, particularly with major hosting companies, where particular subdomains are blessed (www.wordpress.com) and should rank extraordinarily highly, but randomblog.wordpress.com should receive almost no credit from the association with Wordpress. One could imagine StackExchange eventually receiving similar treatment, although whether that would be determined algorithmically or by a hand-issued exception in the Googleplex is anyone's guess.

As a site owner, the takeaway message for you is simple: do not use more subdomains than you can get away with. It will cost you, by splitting your link equity and decreasing all of your pages' potential to rank.

John Conde's answer, which is currently the accepted answer, is wrong because of an overly pedantic emphasis on PageRank, which is both a) a formula which is detailed in a publicly accessible research paper and b) Internet shorthand for "the sum of all algorithms Google uses to rank pages", which is a far wider topic than PageRank proper.

In the sense intended by a question, there is absolutely a difference in Google's treatment of two pages based on whether they are on the same domain or on two subdomains of that domain.

One factor is what SEOs call "domain authority" or "domain trust." A link to any page on a domain says that the linked page is authoritative for the linked topic (the one mentioned in anchor text), and the linked page is authoritative for other topics, and that the linked domain is authoritative for other topics. This is beyond question: it is why Wikipedia ranks for more queries than God, despite not having huge numbers of in-links to newly created articles. It is why a popular blogger is more likely to rank for a newly created article (with no links) than an unknown blogger, even if their title and other on-page factors are identical.

In general, Google is thought to treat subdomains as having a lesser relationship than pages within a domain: they do not fully share domain authority amongst each other. This solves problems like the technique, prevalent a few years ago, where folks would use a profusion of automatically generated subdomains (chicago.example.com, boston.example.com, 67k examples elided, etc) to achieve higher rankings.

This is one of the major reasons why SEOs advise clients to put blogs on example.com/blog rather than blog.example.com .

There are also issues, particularly with major hosting companies, where particular subdomains are blessed (www.wordpress.com) and should rank extraordinarily highly, but randomblog.wordpress.com should receive almost no credit from the association with Wordpress. One could imagine StackExchange eventually receiving similar treatment, although whether that would be determined algorithmically or by a hand-issued exception in the Googleplex is anyone's guess.

As a site owner, the takeaway message for you is simple: do not use more subdomains than you can get away with. It will cost you, by splitting your link equity and decreasing all of your pages' potential to rank.