On page 24 of Gillespie's Population Genetics, 2nd ed, an equation for $H$, the probability that two randomly drawn alleles are different by state, is given.
$H$ is stated to be similar to the heterozygosity of the population, which I guess is expected to be $2pq$, where $p$ and $q$ are frequencies for different alleles. $ H′=(1−1/2N)×H$
On page 23, $H_t$, the probability that an individual chosen at random from the population after $t$ generations of random mating is heterozygous, is given : $$H_t = H_0 \times (1-\frac{1}{2N})^t$$
For a current time $t$, are $H$ and $H_t$ measurements of the same thing, or are they different ?
I interpreted them as being the same, because drawing two alleles at random is similar to drawing a diploid individual at random.