(The answer may vary depending on the research council you apply to, and the type of grant. Let me give my perspective as someone who applied for an EPSRC First Grant last year.)
I don't think that the Je-S form is supposed to be similar to the Case for Support. As you say, the audience for the Case for Support is reviewers, so there you are free to describe your project in detail, using appropriate technical language. By contrast, I think (at least some of) the material in the other parts of the Je-S is intended to be read by non-experts, including non-academics. For example the instructions for the "Summary" component read as follows:
The Summary is used for:
-Sending to potential Peer reviewers to determine whether the proposal is within their field of expertise
-To publicise the Councils research programmes to a variety of readers eg Opinion-formers and policy makers, the general public and the wider research community.
Explain in plain English:
-The context of the research.
-Its aims and objectives.
-Its potential applications and benefits.
In case you didn't see it, on the "Document Menu" page of the application, each item in the left-hand menu bar has a ? button that you can click to get some instructions. (Unfortunately, these instructions don't always clarify things very much.)