SuperDuper is free for doing COMPLETE clones, which is great if you need to do a one-off or are starting a periodic backup routine. However, once you start running periodic clones, you want to do incremental cloning so that only files changed on the computer are modified on the clone. For that, you register and pay the modest cost. Both SuperDuper and CarbonCopy Cloner clones have no special coding for the app. Carbon Copy Cloner can incrementally update clones created with SuperDuper and vice versa. Note that SuperSuper currently does not work with Big Sur, while Carbon Copy Cloner does. Assuming that SuperDuper resolves its issues, both programs are fine for basic cloning and backup. They do have somewhat different advanced capabilities if you wish to explore those.
By the way my history is that I started with CCC when it first came out (and was agressively free). At some point, I saw that SuperDuper had easier to use automated scheduling and switched. Several years late, I ran into an issue trying to update my SuperDuper clones, and, after numerous sessions with support, couldn’t get it resolved. So I switched back to Carbon Copy Cloner (no longer free software, but with improved scheduling). However, I continue to recommend SuperDuper to friends as it is a bit cheaper and has a friendlier interface. I support some of those folks when they upgrade to new computers or operating system releases and have no problems working with SuperDuper or the clones it creates.