actually default file associations are not in the key for file extension, ie in HKEY_CLASSES_ROOT\.pdf\
they are little below in the key HKEY_CLASSES_ROOT, in the key for so called friendly file name - friendly file name is the name in the default value of the extension key, so on the post 1 screenshot pdf_auto_file is friendly name for pdf file
exactly, they are in the subkey shell\open\command of this friendly name key
friendly name is variable, every aplication can create its own friendly name and register by creating key in HKEY_CLASSES_ROOT (but not necessarily change value default in extension key)
but of course default associations are only valid for user account, so one friendly name key often cannot be used as data source for many accounts - if i can judge from my experience primary key for account default association is key
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\FileExts
it is primarily key for context menu open with, but if in extension key in this key are values application or progid with data they are used as default - progid serves as link to friendly name key in HKEY_CLASSES_ROOT; if in extension key is subkey openwithprogid it also serves as default program data source with link to friendly name key; in value application is only application name, not its path, so, i guess, this application must have key in key HKEY_CLASSES_ROOT\Applications for this link to work
to complicate the picture there are keys classes in HKEY_CURRENT_USER\Software and HKEY_LOCAL_MACHINE\Software, that contain some of the HKEY_CLASSES_ROOT keys - friendly name in classes in current user may be other then in classess root, it has preference before HKEY_CLASSES_ROOT; in windows from 8 this key in current user is probably default for user associations
i think explorer searches for ways to open file in account registry hive, if there isn`t specific data in keys in current user it searches for data for opening in key HKEY_CLASSES_ROOT or its copy in HKEY_LOCAL_MACHINE\Software, so actually HKEY_CLASSES_ROOT is last on the data queue list
friendly name key has this advantage that it can serve for many extensions, for exemple various sound\video extension can have only one friendly name
i must add that i am not programmer, these are only guesses from many years of my struggles with windows
while writing this post i tried to check my guesses - i have some docx files, and because i have xp, in
HKEY_CLASSES_ROOT there isn`t extension key for docx - but such key is in Explorer\FileExts, because i added programm for opening docx file to open with - if i just clicked on file it opened in notepad - now i added default programm through file properties - in docx key in subkey openwithprogids appeared value docx_auto_file -
when i restarted regedit and checked in HKEY_CLASSES_ROOT, sure, there is key docx auto file with path to tmviewer; checked second time and in CLASSES_ROOT appeared also key .docx with docx auto.. as friendly name
on post 1 screenshot there is key openwithprogids - i think this is proper key for default application, not persistenthandler, etc - if there is this key with friendly name and another friendly name as default value in extension key default value has priority