I think it’s more of a issue of how “approval” is being used.
“I need appoval from the committee before I begin the project.”
” I am asking your approval to propose to your daughter.”
“I am awating appoval.”
All of these connote agreement, but not necessarily something in writing. It’s more like the result of a vote or meeting.
“I now have an approval (or the approval) in hand.” Here it is in writing. Want to see it?
“The committee finally cave me an approval.” Got in in the mail yesterday. Want to see it.
In short, an approval process ends in approval. After that, you get the approval, or an approval, in the interoffice mail.
Of course, “approval still in process” is memo-ese for “the approval is still in process.” Business people like to pretend that they’re too busy to bother with unimprtant things (like entire sentences).