Well, you can be 'in the process of' writing, of which you can't be 'in the progress of'. And the task of writing can be 'in progress', but I find it less appealing to call it 'the writing is in process'. I think they roughly mean the same, but you can't switch them around at all times. Unfortunately I have no grammar regarding this (which makes this post probably a little obsolete for you, so sorry). :/
'In progress' is a bit more vague, as the process is not named. You normally wouldn't say 'in process', you'd say 'in the process of' and then name the process. 'The book is in progress.' - meaning, something is happening to the book that is moving it along in a process. 'I am in the process of writing a book.' - which is self-explanatory. I hope this helps.
'in progress' is a common expression meaning something is 'in the process of being completed'... 'in process' is gobbledygook... see above for correct use of 'process'...
Not actually gobbledygook -- it's a term of art in supply chain management. But if that were the intended meaning then the writer would know the difference between that and 'in progress'.
ok, so then it's 'gobbledygook' in re the writing/publishing industry, at any rate... and that's what we're dealing with here, right?
Well, a character in a novel who is a production control manager might legitimately refer to items being "in process". In fact, I'm tempted to put a production manager in the next thing I write, just so he can.
I'm pretty sure "in process" is non-standard in most everyday contexts, but I wouldn't know if it's used in business jargon. If you're not too bothered about word order, process and progress mean pretty much the same thing, process being derived from the Old French for 'journey' and progress being derived from the Old French for 'go forward,' ultimately having the same Latin prefix 'pro' used in the same overall context. They just have different connotations which should come fairly naturally to anyone raised in the Anglophonic world.
