They do the same. The logic is that you can supply an argument to enable it (all boolean options are false by default).
If you write some value to the boolean option, it is parsed and checked against (false, 0, off, no) and a match will make it false, any other value will make it true.
The option itself, --full-remote-verification is used to trigger “deep” verification. By default Duplicati downloads the file, and checks that the file hash matches. The --full-remote-verification changes this and actually decrypts the file, opens it, compares the content of the file with the database contents. For dblock files it also samples a random 30% of the files inside the compressed archive and checks that they can be extracted, and that the extracted files have the correct hash.