Yes, there are some significant differences between Home Premium and
Business. And, interestingly, you cannot automatically assume that all
features that are present in lower editions are also present in higher
editions.
For example, Business, which is generally a higher edition than Home
Premium, does not have media center, which Home Premium does have. But
Home Premium does not have remote control or domain networking.
It really, truly is the case that if you want "everything", you just
have to buy Ultimate.