I'm not sure how well this answers the technical problem that you have, but yes, page
screen
and section
all have rather different meanings to me, as an IT Pro.
However the problem that you have, is that the meaning depends on context (doesn't everything?) So, for example, a single PHP file may produce every single visible page on a particular website, so to the site owner, there may be thousands of pages
, but to a back-end developer there is only one page, producing loads of screens
.
'Section' is a little harder - it could mean a small part of a page (there is an HTML element precisely for this) or it could be the equivalent of a chapter in a book, i.e. a whole bunch of URL's.
In older (pre-internet) applications, the usual term for what we might now call a page
is screen
, since the exact size of the screen was usually well defined.