The manual method that you used to analyze your dial 'sound' trace is the simplest form of time domain analysis. You measured the time between transitions between on- and off-states at the zero crossings, and reduced the data for 10 pulses by averaging to yield just one number.

Autocorrelation is a mathematical technique used in digital signal processing (DSP), that is more sophisticated, and relates to frequency domain analysis by the Fourier method, although it is still a time-domain technique.

I am certain this is also the technique used in the Sage Instruments 930A. It uses DSP algorithms for many of its tasks when measuring frequency. When you get some experience with that instrument you'll find that it rarely provides a definitive constant number for the dial speed. There is always some fluctuation. This stems from the nature of the signal, it contains noise and old dials do no rotate with a completely constant speed for every digit. From my autocorrelation graphs you see that the peaks have a certain width, can even have fine structure internally with multiple smaller peaks. Now the question arises which one do we pick as the dial speed ? I don't know what the Sage does exactly, but I suspects it computes some statistic on those peaks, perhaps fits a curve to it, and takes some kind of average after satisfying a set of signal thresholds. The results can vary from time to time, and they do. I have had some dials that even seemed to completely confuse the box, and it was frustrating for this user too. Perhaps an example might be your dial that is mostly fast and partly slow. In these cases, your method of recording these traces and using a spectrum analyzer should explain the situation better, and actually it did!

One more aspect: The trouble with simple autocorrelation has always been that the result is not immune to the harmonics of the true or expected main frequency. Peaks show up not only at their "nominal" frequency, but at twice or other multiples of it. This is avoided by many *enhanced* autocorrelation techniques that mathematicians have developed, some of which are also implemented in Audacity, hence my recommendation to try those. I do have some additional screen shots that I took earlier to select those that I presented. Later...

[PS: for early readers, I misstated the relationship of time and frequency domain in my first draft of this.]