Hello!
What are the benefits and differences between using a NAS vs. a Mac server?
For file storage, backup etc. I think the key question is whether you already have an old Mac Mini with ample storage sitting around that you want to re-purpose as a server. Otherwise, it probably makes more sense to get a NAS, many of which support things like TimeMachine (the support is now in the Samba software, which most NASs use).
None of the recent (last 5 years or so) Mac models are particularly suited for server use compared to a purpose-built NAS (low power processor, multiple internal hard drives, friendly web-based interface so you never need to connect a display) - the M1 Mini comes closest, but then you’ll be paying a lot of money for total CPU and GPU overkill, and relying on external boxes for storage. If you’ve got a spare M1 Mini there are better things to do with it (like, sell it for cash!)
The only exceptions for home/personal use are things like iTunes/Music sharing - there have been third party iTunes-compatable media servers, available with some NASs, but in my experience they tend to break with OS upgrades and turn into abandonware - so if that is important it might be a reason for using a Mac server. However, Music etc. is now pushing everybody to the cloud and if you have an extensive local media collection you will probably be looking at things like Kodi/MrMc and Plex which can happily use NAS as a media store. One case for having a more beefy processor in the server is for systems like Plex that can do on-the-fly transcoding, but even that’s not such a big deal if you’re serving modern devices that support most formats over a fast network.
For office “workgroups” etc. I seem to recall that Mac Os Server (even after it turned into an App) had some features for managing Mac workgroups with user accounts, iphones, mail etc. but a lot of that is obsolete or taken over by cloud services now, and for serious business there are various cloud/Linux-hosted Mac/iOS “fleet management“ tools available now.
Personally, years ago, I got a cheap HP “home server” box, installed Linux on it and used that, and it’s still going strong - but then I like messing with Linux... buying a ready-to-go NAS seems more practical.