What is the difference between adding a custom property via the Object Data tab vs the Properties Shelf? In Blender 2.82a, on Ubuntu Studio 19.10, there would appear to be a place to add custom properties other than under the Object Data tab of the Properties Panel. Under the Tools tab of the Properties Shelf (N-Panel), there is seemingly another place to add them:



I am not clear on what adding them using this other method actually does, because I have found that, for any object currently selected which has had custom properties added via the Object Data tab, those custom properties cease being displayed in the Properties Panel as soon as that object is no longer selected (as one would expect, since the context has changed).

When custom properties are added via the Tools tab of the Properties Shelf, then unselecting the relevant object does not stop the custom properties from being displayed in the corresponding location of the Properties Shelf. Instead they remain visible. I am wondering why this is.

It would appear that adding the custom properties in these two ways is doing something different, and that these two approaches are not merely two different ways to do the same thing.
Custom properties are always associated with a data block they belong to.
The place you add them from determines which datablock they are associated with.

Adding custom properties through the Properties Window will make them associated with the datablock of the currently selected tab.

You can add properties to Objects, so selecting a different one make them "disappear", but you can also add them to Object Data so several instances of the object sharing that data will have the same property.

You can also add them to Materials or Scene, Textures, Particles, among others, regardless of the object they are applied to.

Likewise custom properties added through the Tool tab are associated with another type of datablock, in this case not dependent on selected object, but the current Workspace.
Workspaces are represented by the tabs at the top, an are themselves datablocks that can be linked to or appended, and can bear their own custom properties.