Since different Analytics Edge add-ins interact with your workbook in different ways, they will prevent multiple Analytics Edge add-ins from running at the same time. This means if you install the Basic Add-in and the Core Add-in, only the Core Add-in will appear. To get the Basic Add-in operating, you need to uninstall the other add-ins.
The Analytics Edge add-ins will defer to the more-complete version, so the Core Add-in will appear first, and if it is not installed then the Standard Add-in will appear, and if it is not installed then the Basic Add-in will appear.
Note that if you have multiple Analytics Edge add-ins installed, scheduled refreshes may leave a copy of Excel (with no workbook) open after a refresh. Uninstalled the unused add-ins to stop this behaviour.