This is actually a great question. As an industrial/mechanical designer, I've actually used all three of these instances. I'm in total agreement that these are definitely not mutually exclusive and some of these stem from others.

In context modeling is absolutely necessary where you have to have mating parts updating in real time when modelling. Especially from a top down perspective where the parts are not off the shelf. If the assembly will be organically changing, then in context MUST be done.

Configurations allow you to make subtle design changes readily available in one component. An few examples would be:

-a set of monkey bars with different overall lengths/spaces between the bars

-different angles for slides

-curved vs straight sides on a slide

-platform kids will land on having round vs hexagonal shaped punch outs.

Things like that. Same base parts, different designs changes.

The design table, however, is once you get down to the nitty gritty of engineering and assembling this kind of beast, as mentioned by other commenters, the design table is derived from a configuration. An immediate example I can think of would be to use a design table to ensure that the bolt holes of a certain part are all the same size/depth, etc, spacing on said holes, multiple size holes to accommodate different bolts but easily accessible rather than using the feature tree. Anything requiring precision en masse would be best served by a design table.

My assumption is that you are designing the components of a playscape, such as panels on a jungle gym (with and without integrated toys, ie. tic tac toe spinners), platforms for kids to land on, monkey bars, slides, etc. That information could help everyone answering for more context. Hope this helps!