According to the Yoshida Doctrine, Japan would try to build its own economy while letting the U.S. provide for its security. Of course, this is the opposite of what Hatoyama said he wanted – a more equal relationship.
In reality, the main difference between the two approaches was mostly in the words used by the Japanese politicians and the Japanese media. Under the Kan administration, in their words, they would always stress the importance of the relationship between Japan and America – that was their tatemae (建前), their façade they put on when dealing with the rest of the world. But their honne (本音), their true feelings, was still with their neighbors and the desire to build an East Asia Community.
During the Kan administration, Japan would implement a policy called seikei bunri (政経 分離), the division between politics and economics. This policy goes back to at least the Nixon administration. Under this policy, regardless of how bad the political relationship between Japan, China, and Korea became, Japan would nonetheless try to improve its economic relationship with those countries and thus build its East Asia Community. I imagine the first time Japan tried to explain this policy to America, the conversation went something like this.
Japan: You guys have the division between church and state right?Not surprisingly, relations between America and Japan did not improve under the Kan administration.
Japan: Well, we have the division between politics and economics. If you guys can have a division between church and state, we can have a division between politics and economics.