Ok, I think I've figured it out.
If you have turned on the Accessibility feature Larger Text, and upped the text size a bit then the Calendar view changes. Probably to make room for the larger text. Larger Text depends on an iOS feature called Dynamic Text that allows other apps to change their text size based on system settings.
Calendar did not respond to this settings under iOS 8. It looks like it does under iOS 9. So if you had experimented with this settings in the past and left it larger than normal, then the change probably happened with the update. I'd heard that Apple had expanded the use of Dynamic text throughout their apps, but forgot until I saw your screen shots where the text is larger than my screen shot.
Go to Settings > General > Accessibility > Larger Type, and make sure the slider is in the middle. Even one step above will change the weeks displayed to five days. The max will take it all the way down to four days. The "Larger Accessibility Sizes" switch should be off.