Because people like to define these terms to suit their purposes, there are many different definitions of eBusiness and eCommerce. We define eBusiness as completing primary business functions online.Some examples might be eMedicine, an online brokerage, or perhaps a SaaS application.
eCommerce is eBusiness but more specifically the online purchase of physical products. Amazon is both an eBusiness and an eCommerce business. Their services like Amazon Prime Video and Amazon Web Services are eBusiness where their core shopping business (and where they originated) is eCommerce.