Can someone please help with scope terminology? Some scopes have "analog" and "digital" channels. Am I right in thinking that the "analog" channels are in no way similar to the old Tektronix 475 I used to use at work, but are sampled/interpolated etc.? In which case, why are the "digital" channels different? It's pretty clear that none of the modern scopes have CRTs. Is it just that the digital channels are similar to logic probes and resolve to zero and one?
For sampling analogue waveforms, even digital waveforms if you want. The signal is passed through an ADC to convert it to a quantized value which is displayed on screen
These are used for logic analysis. They are not passed through an ADC (well they may be but anyway), but are rather fed through an analogue comparator with some reference level producing a low or a high. These are then plotted on screen.
Analogue channels are expensive, especially if they are high sampling rate. You need an ADC with enough bandwidth and then the raw processing power to display the signals. However they are also very useful as you can see the full signal as a representation of voltage vs time. You can even do math functions like FFT.
Digital channels are cheap. Analogue comparator hardware is easy to implement, and because they are only 1 bit (high or low), the processing power required is much less. However you can't see what the signal looks like, just whether it is above or below a threshold. Even still, they are very useful for analyzing something like a 16 channel data bus. For example a 16 analogue channel scope would be hellishly expensive compared to one with 16 digital channels, and if you are only interested in the digital value of a signal, not what the voltage waveform looks like, then digital channels are a much simpler way of measuring it.
In short, analog channels are connected to a analog to digital converter. Digital channels are connected to a comparator which will tell you if the channel is higher or lower than your reference voltage. Which is cheaper? The fast ADC's run in the hundreds to thousands of dollars (and you may need to parallel them if you want to sample faster). Comparators are cheap - tens of dollars and then a dac to set the voltage your comparing.
You have it right. The analog channels feed an attenuation stage followed by an analog to digital converter and its associated memory for storing the sample record. Commonly now called an MSO (mixed signal oscilloscope) such models can typically include 16 logic channels that record just 1 bit of information on each digital channel for every time sample. The digital logic channels are like a logic timing analyzer that is correlated to the same time base as the analog channels. Visually you see analog waveforms with some shape and square waveform shape for the digital channels, all time aligned.