Power Pivot

The PowerPivot add-in is a data analysis tool which provides an extension to Pivot Tables.
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.
www.microsoft.com/en-us/download/details.aspx?id=29074

Manage - Displays the separate Power Pivot application window allowing you to load and prepare data or continue working on data already added to this workbook.
Measures - Drop-Down. The drop-down contains the commands: New Measure (previously New Calculated Field), Manage Measures (previously called Calculated Fields)
KPIs - Drop-Down. The drop-down contains the commands: New KPI, Manage KPIs.
Add to Data Model - Create a linked table by adding this Excel table to the Data Model. Linked tables are a live link between the table in Excel and the table in the Data Model, so any updates to the table in Excel automatically update the data in the model. If this table is already in the data model, this action adds a copy to the data model.
Detect - Automatically detect and create relationships between tables used on the selected Pivot Table.
Settings - Displays the "PowerPivot Settings" dialog box. Define settings for your Power Pivot environment and specify language options.

If the "Microsoft Power Pivot for Excel" COM Add-in and the "Microsoft Power View for Excel" COM Add-in are both ticked pressing the Manage command will display the Power Pivot for Excel window.
If the "Microsoft Power Pivot for Excel" COM Add-in is not ticked then pressing the Manage command will display a prompt saying "Enable the Data Analysis add-ins to use this feature". Pressing Enable will effectively do the same as manually ticking these add-ins in the COM Add-ins dialog box.

Not Available To Everyone

This add-in is only installed (by default) for the following Microsoft 365 subscriptions:
Microsoft 365
Excel 2021 standalone
Excel 2019 standalone
Excel 2016 standalone
Excel 2013 standalone
Excel 2010 standalone (not installed by default, must be downloaded separately)

Power BI

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
Advanced calculations
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.

COM Add-in

Name - Microsoft Power Pivot for Excel 
Location - C:\Program Files\Microsoft Office\root\Office16\add-ins\PowerPivotExcelAdd-in\PowerPivotExcelClientAddin.dll