No, NTP and PTP are two different protocols. They can both use hardware timestamps and reach single-digit nanosecond accuracy in ideal conditions. The main difference is in existing support in switches and routers, which is needed to avoid the impact of asymmetric delay between ports (typically tens of nanoseconds per switch).
PTP has good support in higher-end switches and routers, but it's difficult to secure and make resilient to failures. It was designed for automation and control networks in factories etc. NTP is a better fit for computer networks, but there doesn't seem to be any switches or routers with HW NTP support. If you really need the best accuracy with NTP, you can find old 100Mb/s hubs on ebay and create a separate network.
Yes, PTP and NTP are indeed very different protocols.
There's no networking hardware timestamp support for NTP because NTP has nothing to do with hardware timestamps.
PTP can be done without hardware timestamps, but it was designed with hardware support in mind.
I don't know where you got it that NTP does anything even orders of magnitude close to nanoseconds:
> NTP can usually maintain time to within tens of milliseconds over the public Internet, and can achieve better than one millisecond accuracy in local area networks under ideal conditions
> The Precision Time Protocol (PTP) is a protocol used to synchronize clocks throughout a computer network. On a local area network, it achieves clock accuracy in the sub-microsecond range, making it suitable for measurement and control systems.
> There's no networking hardware timestamp support for NTP because NTP has nothing to do with hardware timestamps.
Both NTP and PTP don't care (as protocols) where the timestamps are coming from. That's an implementation detail.
> NTP can usually maintain time to within tens of milliseconds over the public Internet, and can achieve better than one millisecond accuracy in local area networks under ideal conditions
That was maybe 20-30 years ago, but not today. The wikipedia article needs an update. If you don't hit a routing asymmetry, in my experience it's usually milliseconds over Internet and tens of microseconds in local network if using SW timestamping. Please note that NTP clients by default use long polling intervals to avoid excessive load on public servers on Internet, so they need to be specifically configured for better performance in local networks.
Note that this is for the system clock, which has to be synchronized over PCIe to the hardware clock of the NIC. That adds hundreds of nanoseconds of uncertainty. It doesn't matter if the hardware clock is synchronized by PTP or NTP.
If you care only about the hardware clocks, it's easy to show how accurate is the synchronization by comparing their PPS signals on a scope. NTP between two directly connected NICs, or a with a hub, can get to single-digit nanosecond accuracy. I have seen that in my testing. It's just timestamps, it doesn't matter how they are exchanged.