"Number of Persons” Vs “Number of Person-years” in a Stationary Population

I have learnt that the life table function nLx is the number of "person-years" lived by the cohort between ages x and x+n.

But for stationary population, nLx is defined as the number of persons in the population who at any moment are living within the age interval (x, x+n).

I don't understand, for stationary population, why is nLx number of persons , rather than number of "person-years"?