Probably the major difference between business administration and public administration lies in the difference in the organizations and purposes being administered.
Business administration involves the administering of a business, an entity that, by definition, has been created with the goal of making a profit for its owners or investors or both. Business administration, therefore, focuses on those decisions that will contribute to the realization of this goal: how to obtain resources efficiently and at lowest possible cost; how to produce goods or services and how to market them effectively to identified markets; how to manage personnel so as to support production and distribution while minimizing costs; and so forth.
Public administration, on the other hand, infers administering services for "the public" - that is, all citizens of a community. The goal is to provide services supporting the lifestyle needs and wants of the community, not to make a profit. Public administration is usually financed by taxation, which may increase or decrease with impacts on the amount or type of services that can be provided. Products and services are provided to a much wider market - all citizens - but there still is consideration of how to do so economically and efficiently.