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They are definitely measured differently. The insert window you would measure inside the existint window frame, which in most cases is built out of 3/4" lumber all the way around. For a full replacement window, you can remove the interior casing and include that frame within your measurement. In regards to our answer, better late than never. If this process becomes a pain in the "sash" simply consult a professional. Make it a great day!
Hello Geoff,
In fear of giving you information that is obvious or that you already know, we move forward boldly and answer this question. I had a similar addition on a previous home and it was difficult to keep it cooler in the summer months. What ended up proving helpful was to put a small box fan on the floor outside of the room to draw the home's air conditioning into that space. That teamed with controlling the sunlight with window treatments proved effective. Thanks Geoff!
I would concur with the above answers. If you are able to fill with wood putty and paint that would prove to be the most cost effective option. If you would like to go further, determine the brand of the door and I'm sure you could find a replacement sash. I am like you, I love my dog like my children, continue to be patient and show your bowser the love he deserves.