In macOS settings, what is the difference between apps accessing to iCloud vs iCloud Drive
There's really not much difference, but the way to generally look at is:

iCloud is all the behind the scenes things like settings, scripts, messages, etc.

iCloud Drive is the user &quot;usable&quot; front end where you can directly access files and such as you normally would on a computer.


Let's use Photos as an example... You don't really access Photos either via the actual photo files nor do you really need access to the Library (database) file.  All of this happens behind the scenes and you access your Photos via the Photos app whether it be on your Mac or your iDevice.  A third party app (Lightroom for example) would want access to your Photos so it might ask for permission to use &quot;iCloud.&quot;
Looking at a different (random) app, maybe you get a &quot;Journaling&quot; app that lets you chronicle the day's events.  It saves it in a Rich Text format and can use any number of online services like iCloud Drive, OneDrive, DropBox, et al.  That may ask you for access to &quot;iCloud Drive&quot; because it's saving a file in the more traditional sense - to a common location where you save documents.
Going back to Mail, it may need access to both.  It will utilize the mail back end of &quot;iCloud&quot; to synchronize mail across the devices or access contacts, but will also utilize &quot;iCloud Drive&quot; as a place to save and get attachments.
I applaud your diligence in questioning what Apps are asking for and this is an excellent line of questioning.  What you should also be looking for is what the app in question is accessing when it accesses iCloud or iCloud Drive - i.e. Contacts, location, mail etc.  I was recently looking for an IP subnet calculator (a networking thing) and it wanted access to my Photos and Location.  Needless to say, it didn't get downloaded.