Copying files: does Windows write to disk if files are identical?

Robocopy.

Windows cannot differentiate between identical and modified files if you copy using Windows Explorer.

Windows can differentiate between identical and modified files if you copy using Robocopy, which is a file-copy utility included in Windows (Vista, 7, 8.1 and 10).

There's no need to use third-party tools.

You can save this script as a batch file and re-run it whenever you want to perform a backup:

robocopy /e c:\PDFs p:\PDFs

• Whenever a PDF file is annotated and the changes are saved, both its Last Modified and Size attributes will change in the source folder, triggering an overwrite of the corresponding file in the destination folder the next time Robocopy is invoked.
• Robocopy compares the Size and Last Modified attributes of all files that exist in both the source and destination. If either attribute is different, then the destination file will be overwritten. Note: these values only need to be different, not necessarily newer or larger; even if a source file has an older Last Modified or smaller Size attribute, the source will still overwrite the destination.
• the /e (or /s) switch isn't necessary if all of your PDFs are in the root of the folder referenced in the script but if you want to include Subfolders then use /s. If you want to include subfolders and Empty subfolders, then use /e.
• I would assign the backup drive a letter further along in the alphabet, so there's no risk of another drive being inadvertently assigned the drive letter used in the script, causing the backup to fail at some point in the future. I used P here for PDF.

That simple script is all you need.

Windows does not do this. It will however prompt you to overwrite files with the same name and you can select manually if you want to do it.

For a easier solution, use FreeFilesSync to compare the folders and overwrite only changed/updated files (Mirror option and select File time and size in Comparison Settings).

Yes and no! Windows Explorer only checks for metadata (file size, dates etc.).

But you could use a script e.g. powershell (see here) which comes with (most) Windows or 3rd party tools that let you compare/copy files using file checksums e.g. MD5 or SH1 hashing (see here and/or use a search engine).

I myself like to use the software checksum compare (see here), it lets you compare files and directories including file checksums and it works from a USB pen drive.

If you don't need to compare the file's content and if you just want to copy "newer" files you can use any advance copy method like xcopy, robocopy, etc.

Note: the different hashing methods have up and downsides (mainly reliability vs. speed). For me MD5 is more than enough for this type of file comparison, but that's a personal preference. See here for further info on that topic.