Synology is a VMS and one nice thing about VMS is that they're a little more camera brand agnostic than NVRs are. If you buy a NVR from Company A then decide a few years down the road you want to buy a camera from Company B that has some new cool advanced AI motion-detection feature that reduces false positives, you're almost guaranteed that the NVR won't be able to access the advanced features on that camera. With a VMS like Synology or BI, you at least have a chance. Take Dahua IVS, an advanced camera feature. Granted, Synology users here had been filing support tickets asking for this feature for over four years, but Synology finally added it. IMO you'll never see a NVR not made by Dahua support the advanced features built into many Dahua cameras. Replace Dahua with Hikvision in that last sentence and it'll still read correct.
NVRs generally don't have enough processing power to do their own motion detection; they rely on the cameras to detect motion and notify the NVR when that happens. This means with a NVR your motion detection abilities will vary by your cameras capabilities. For example, my older Dahua 5231s and newer 5442s both have IVS, but only the newer 5442s have the AI filter that can only trigger when motion is identified as a person and/or vehicle. Using a NVR, I don't have a way to supplement the older 5231s to make them better. Most VMS give you the option to additionally monitor the camera stream and run another lay of motion detection. My experience using an older Synology for this wasn't good -- one camera overwhelmed the processor, slowing down the Synology to where NAS-related things were affected. Also, Synology's built-in motion detection (again, this was a few years back) wasn't any better than than the basic motion detection built into cameras ... i.e. wasn't even at IVS level. Maybe that's improved.
Blue Iris has some pretty robust motion detection features that can usually meet or beat Dahua IVS. This can be handy because while Dahua cameras often have multiple features like IVS, People Counting, Face Detection, Heat Maps, etc, the camera itself can usually only be configured to do one of them. So you often can't have it do IVS and Face Detection at the same time. With a VMS, you can have the VMS do IVS-like motion detection (if it's capable, I know BI can) and then have the camera configured for Face Detection. There are also at least two open projects floating around in threads here where you can install an AI engine on your BI PC and have BI alert images filtered through there.
If you want your camera system to interface with other systems in your house (like one of the many open-source home automation systems), doing that with a NVR is a lot harder. VMS like Synology/BI can take custom actions when a camera senses motion, like doing an HTTP GET/POST across your network to your home automation system with a parameter in the URL that lets it know which camera had motion. This makes it possible for HA systems to do an automation like "if the driveway camera senses motion after dark and the outside lights aren't already on, turn them on for give minutes, then turn them off". BI will even let you run any script or executable, which makes what you can do when motion happens pretty much limitless. I haven't seen a NVR that can send alerts across the network like this. There's the option of paying a bit more for a model that has IO ports on the back, then physically wire those ports in a manner that whatever system you're connecting to can read them. Even then, the NVR can usually only generically say "motion was detected" and can't be specific as to which camera detected motion, which limits a lot of the usefullness IMO. I have seen some folks setup a script on another box running 24/7 that polls the NVR or cameras for motion detection and then forwards that over to the HA system.
I started with a Synology for a few months back in 2016, moved to a Dahua NVR for a few months, then have been on Blue Iris for the last several years. When I started my camera system, I absolutely did not want an always-on PC involved in the project. Since I already owned the Synology and it came with two free camera licenses, made sense to start there. It did not support IVS back then and I could not tune basic motion detection to reduce false alerts worth a damn. I also didn't care for the smartphone app UI or speed, but hopefully that's changed since then. When I added my third camera I had to choose between paying for a Synology license or buying a Dahua NVR. I really really really wanted more reliable motion detection (IVS) so I went with the NVR. IVS significantly cut down the amount of false alerts. I disliked the Dahua smartphone app even more -- it was slower and more cumbersome to see if any recent motion had been detected. The NVR was a newer model back then and had some firmware teething issues (all since resolved), so as a temporary backup to the NVR while the issues were being worked I installed the Blue Iris demo on an old PC that was laying around. When I saw how easy its web interface and smartphone app made it to see recent events/live views, I was sold. Again, I went into this absolutely not wanting a PC running 24/7, but after seeing how important the camera system had become to folks in the house and how much easier it was to interact with it from smartphones/computers with Blue Iris, that was that. I'm sure (or at least I hope) both Synology and Dahua have significantly upgraded the UI of their apps since my last experience with them.
If Synology had supported IVS when I started, it would have reduced a lot of the friction that caused me to leave that platform. I still have my old NAS running, I'll have to down the latest Surveillance Station build and iOS app and see what's changed. Now that I'm on Blue Iris, I can't imagine using anything else, but it was a long road getting here.