Design tables, as in embedded Excel documents that create/edit configurations are only available in the 3D model, not the 2D drawing.
I'm not familiar with any "easy" way to show all the configurations of a given 3D model in a 2D drawing. Mostly because a drawing view points to a given 3D model of a certain configuration............
Perhaps the best (not linked) way is to copy and paste your Excel document from the 3D model into your 2D drawing.
I can provide a couple of examples if you are willing to attach your example files.
Yes, I believe you do have insert a "real" design table for it to be available for drawing insertion.
The config dim table is a simplified design table for when you don't need the full power and complexity of a design table.
Insert an auto-create table and I believe it will build off what you have.
Kevin is correct, I never heard of/tried that before. It is possible to insert the 3D model Excel based design table in the 2D drawing. I however can't seem to get it working on my computer, but the SOLIDWORKS help says it's possible.
What you have in your part is not a design table.
A design table is a microsoft excel file which is built within solidworks.
For adding a design table you can go to Menu - Insert - Tables and select Design table in your part.
Once you have a design table in your part you can add it in your Drawing too.
What you have in your part is not a design table. I think it's called configuration table and you can not add it to your drawings.
You can read here more about design tables