I think a slightly better term is "discrete" vs "continuous". Some analog clocks are discrete, some are continuous. Some digital clocks operate on a resolution so fine that they appear to move continuously. It's quite lovely to find those that invert your expectations when out in the real world.
There are analog clocks where all hands move continuously (like when there's a second hand with no discernable beats). There are analog clocks where all hands move discreetly once per second (60 BPM for all hands). There are analog clocks where the minute hand moves at 1 BPM (quantized to the floor of each minute) while the second hand does something else (perhaps discrete movement at 60 BPM, or perhaps continuous other than a pause at the top of each minute, etc.). And there are digital clocks!
You're correct, thanks for the clarification. I was going more with the colloquial understanding of the two (analog = continuous; digital = discrete) and was trying to touch on the vagueness of no true analog clock with the reference to ticks/resolution.
However, your explanation is definitely much better.
A digital clock is 1:01 or 1:02. An analog clock is some tick of some range (depending on the resolution, as you abstracted), at all times.