Personally, I take "enterprise" application as application used in an organization that has a medium to large size, and the application is used across the organization, to support its main business functionality. The failure of the application usually has a serious impact on the organization's main business.
Although complex business requirements usually end up with having a complex system to support it, it is not the complexity of the system we used to measure whether an application is "enterprise". (That's the result, but not the origin.)
For example, the supply chain system I am working on now, I consider it as an enterprise solution. If it fails, the company cannot order from vendors, thus has nothing to sell and make profit.
During the implementation of the project, I made some tool to generate DCO/DAO's for myself, this tool is obviously not an enterprise solution, even if I share it with other developers.