When you take ownership of a workset it becomes editable to that user 'Yes' and when you relinquish the workset it reverts to 'No' (which doesn't actually mean you can't edit it).
WorksharingUtils.CheckoutWorksets allows the user to take ownership of the workset and make them editable to that user.
WorksharingUtils.RelinquishOwnership allows user to decide via RelinquishOptions what is relinquished (given back) including various workset types.
I believe the 'editable' indicator is just a function of if the current user has taken ownership of a certain workset or not i.e. they can take ownership of a workset for whatever time period to be sole editor of it until they relinquish it. The 'Yes/No' is only meaningful when you are the owner of it. The interface is probably outdated and contains bad terminology to a certain extent. The default is 'No (Non Editable)' meaning everyone can edit items on a workset via borrowing elements (so 'non editable' means you can edit it and so can everyone else).
I believe the only other time it is 'yes' is when you've just created a workset but are yet to synchronise it to central. You can't make it 'non editable' available to all users until after you've synchronised it (because it doesn't yet exist in the central file). So under that circumstance you would have to synchronise then relinquish. Similarly if you wanted to rename a workset you would have to make it 'editable' first.
So in summary the 'Editable/Non Editable' aspect should be read as relating to if current user can solely edit the workset or not rather than just being a borrower of elements on a workset.
The 'Owner' column exists separately from the 'Yes/No' one because some types of workset you decide to be the editor/owner of (user created ones) whereas when you create a view the ownership of the view workset is inherently you until synchronised.