The PowerPivot add-in is a data analysis tool which provides an extension to PivotTable functionality.
This add-in allows you to work with more than 1,048,576 rows and can work on data from multiple sources.
Fast manipulation of large data sets, streamlined integration of data and the ability to share analysis through SharePoint.
This term is a very general and very loose term.
It refers to the ability to connect to on-premise and/or cloud sources and incorporates SharePoint Online.
This encompasses both Power Pivot and Power Query.
More Powerful that Pivot Tables
This extend the capability of the PivotTable functionality with new features such as
Expanded data capacity
Import data from multiple sources
Publish workbooks as interactive web applications
Use the Data Analysis Expression (DAX) language to create advanced formulas
A powerpivot data model can be used to create a pivottable.
PowerPivot provides a "self-service" approach by allowing users to easily connect to different data sources to analyse data.
PowerPivot does not replace SQL Server Analysis Services (SSAS).
There is also a Power Pivot window and a Power Pivot Field.