Planck Time

I find the concept of Planck Time to be very intriguing. Basically, it is defined as the time it takes a photon, in a vacuum, to travel the Planck Length (1.6E-35 meters). In other words, it is the shortest realizeable period of time in reality. Does this mean that time is actually digital? Just that the devices we have to measure it whether they be our minds or our atomic clocks just can't resolve down that far? If nothing exists between tics of the Planck time, how do you seperate one from another? I think of time as more of a concept rather than a physicality, but none the less it is fun to think about.