EDIT mode page shows different fields and sections than VIEW mode page does - why?

Check if there is more than 1 form for that table. Maybe there is one form being used for View and another for Edit in form settings.

Other than that, it pretty much has to be Form rules.

OK thanks.  I guess it has to be a form rule because I am using same form for both VIEW and EDIT for that role.  Guess next step is to figure out which rule.  My initial review of rules does not appear to have anything that would affect this, but will play around with disabling rules that had the missing sections in it to see if that makes a difference.  Will keep this updated until I figure out what my issue is.

Also double check your form elements in the form settings as you can set fields to only show in view or edit 

Thanks to both of you for your responses...

I figured this out finally, and discovered I had 2 issues:

1. The Section in my form containing the Field in question, was hidden for editing to the users in the role I needed to grant access to, but only for one of the users in that role  So I copied the role, renaming it to something relevant for the new role, then assigned the user to the new role.  This made the Field visible for the user, but did not allow editing even though the role permissions had the Field set to modify.

2.  I then discovered the Field in the table also had further permissions for the defined Field itself.  After setting the Field permission for the role to modify (below), all started working as expected.

My Problem:  I mistakenly believed these permissions were linked to the role permissions, and I did not realize editing the Field access under roles, did not affect the permissions defined in the tables Field.