shapefile - What is hierarchy (object model) of features in ArcGIS?

I'm new to GIS.

My understanding of shapefiles is that they are (contain?) featureclasses, that contain features (points, polylines, polygons). Is there a clear hierarchy for these files. Would the next level after features be individual points? Are polygons and polylines merely point collections? What implication does this have for working with the data - e.g. can all geometries be worked with at the "point" level?

Is there a resource that would help me to understand the data structure and/or object model of these files? What I am essentially looking for is an explanation as to what exactly shapefiles are and what I should know when working with them, especially when using ArcObjects. In addition to this - how does this relate to other software like QGIS? Do they operate in the same way?