As was mentioned before, M.2 is only a form factor.
But to go with your samsung examples you can check out the following:
The "original" 2.5" Samsung EVO 860 is the common SATA drive.
The M.2 Samsung EVO 970 is the M.2 drive using NVMe (~PCIe), so the fast one.
There is also a cheaper version for the M.2 though which is the M.2 EVO 860. This is the slower one, using SATA and also still has the SATA name scheme (with the 8XX).
Regarding Speed: Yes, M.2 NVME are faster, but the real life performance isn't that much better due to other factors which take up loading time.
So while the switch from a HDD to SSD is like switching from walking to driving to the next city, the additional time gain by switching from a SATA to NVMe is like switching from a toyota corolla to a porsche. Yep, the porsche is much faster and has much more PS. But in the end, both have to wait the same time at a red light and have to follow other rules. In most cases the difference will be negligible.
Now the latest AMD boards also have support for Gen4 M.2 drives which are supposed to be even faster. However they need additional cooling and well…they thermal throttle quite a bit if you actually use their full speed over some duration and in games the difference is basically non existant.
In this video by overclocker Der8auer you can see the SATA M.2 SSD VS NVME M.2 SSD VS Gen4 SSD
So in the end, there is a slight advantage of M.2. NVMe, which you will probably not realize in the real world. But the price difference is also getting lower and lower so you might just want to get it. The new generation (if your board supports it) doesn't seem to make any sense at all atm.