What's the difference between measurement resolution and digits per second in time measuring devices
Carmel Instruments products page for time interval analyzers / frequency counters explains it as follows:


  Freq. Resolution - The resolution for Frequency Average and Period Average functions is dependent on the single-shot time resolution and the duration of the measurement (effective gate time). It is easier to specify it as a number of digits per second. For example, 12 digits/s means that you will get 12 digits of frequency resolution with a 1 second gate time, or 9 digits in 1 millisecond. If the signal input is 1 MHz, 9 digits of resolution translates to 0.001 Hz resolution.


So some of the comments were on the right track. I note that this specification gives no indication of accuracy and, as posted in the comments.

Back to your question:


  What's the difference between measurement resolution and digits per second in time measurement devices?


According to Carmel there isn't a difference other than it is easier to relate meter resolution to time interval when using digits per second.