A digital scope is either a real-time scope (aquires the waveform in real-time) or a sampling scope (i.e. it acquires the waveform over multiple acquisition passes).
Great! So depending on the time/div setting and the input frequency content or bandwidth limiting, a DSO could be either. Or maybe all of those DSOs which can operate either way are a myth. That sure unambiguously simplifies things.
Both the 2230 and the 7854 are are analog/digital combi-scopes which both reach their analog BW in repetitive sampling or analog mode only. You're right that none of them are true sampling scopes as they are combi scopes with an analog and a digital mode.
The analog capability of these oscilloscope is irrelevant to the discussion. Why bring it up?
And you are flat out wrong. Neither of these oscilloscope are bandwidth limited below Nyquist. The bandwidth for both is independent of sample rate. This is easy to demonstrate by making an RMS noise measurement at different sample rates; lower sample rates which cause aliasing do not change the measured amplitude because the input bandwidth does not change. The same measurement made of a sine wave or any other signal will produce the same result. Some DSOs take advantage of this for their external calibration.
So what distinguishes a sampling oscilloscope like the HP 54120B or Philips PM3340?
Back in the old days, Tek used to define1 a sampling scope as a scope that put the sampler in front of the amplifiers and a DSO as a scope that has amplifiers in front of the sampling stage. But this was never an universally accepted definition and wasn't even correct as not all sampling scopes followed Tek's definition (i.e. LeCroy WaveExpert and I believe also the Agilent/Keysight DCA-J/-X). HP also had some sampling scopes (i.e. the 54501A) which didn't follow Tek's rule as well.
Today, a sampling scope is generally considered a fully digital scope that acquires its waveform over subsequent acquisitions to reach its full analog BW. It doesn't matter what sampling technique is used (random or sequential), or how it is actually implemented.
If the marketing departments of other companies want to confuse the issue, that is up to them. One reason they did so is because sampling oscilloscopes were traditionally difficult to use which is why the Tektronix 7S14/5S14 were designed with a built in delay line which is the primary thing limiting their performance. The delay line was either external or optionally built into later Tektronix sampling oscilloscopes. The Philips PM3340 has a delay line as well limiting its bandwidth to 2 GHz but making it much easier to use.
The HP 54501A is just another digital storage oscilloscope with analog triggering, a bandwidth of 100 MHz, and a sample rate of 10 MSamples/second making it comparable to a 2230 or the 11403A being discussed except for the exceptional bandwidth of the 11403A. The comparison with the 11403A is apt because both HP and Tektronix fell into the "one big knob" user interface trap at that time. In the future, one big knob will control everything!
The definition that Tektronix used has the virtue of being less confusing but even they later limited it to the product descriptions instead of the product names leading to things like "communications signal analyser", "digital signal analyser", and "digitizing oscilloscope" which could mean anything including a 7104 with a digital camera or a scan converter.
So what distinguishes the performance of a sampling oscilloscope from your examples? Overload recovery time is one. Sampling oscilloscope have no overload recovery time which is very useful or even indispensable for some measurements. If I want the best overload recovery time, then I want a sampling oscilloscope no matter what they are calling it today. Picotech makes some and they even call them
sampling oscilloscopes. Everything else they make is unambiguously real time but some of their Nyquist bandwidths are not much higher than their input bandwidths; I much prefer ETS support when that is the case.