Hi Penny,
I realize this thread is a few months old, but thought I would add some additional info about ArcGIS Online and Portal for ArcGIS.
Esri's software strategy is the idea of "Web GIS", a pattern for delivering GIS capabilities. One of the key concepts behind web GIS is that all members of an organization can easily access and use geographic information within a collaborative environment. Analysts still provide technical GIS expertise in the traditional sense, but other staff in the organization with little or no GIS knowledge can also benefit from and contribute to the organization's GIS platform. Web GIS leverages existing GIS investments and makes them discoverable and more accessible. It provides a platform for integrating GIS with other business systems and promotes cross-organizational collaboration. Consequently, web GIS extends the reach of GIS to everyone in an organization, enabling better decision making.
Implementing Web GIS | ArcNews
You can deploy "Web GIS" in the cloud using ArcGIS Online, or in your own infrastructure using Portal for ArcGIS (a component of ArcGIS Enterprise/ArcGIS for Server). As others have stated previously, the ArcGIS API for JavaScript is an API that enables you to develop custom client apps that consume and work with GIS resources (typically web services) in the "Web GIS".
Hope this helps,
