The language around this is tricky. That’s why I like writing things out in math. If there are M groups of effects with N_m members each, and you have a prior like this
\qquad \alpha_{m, n} \sim \text{normal}(\mu_m, \sigma_m) for m < M, n < N_m,
and then hyper priors like this,
\qquad \mu_m \sim \textrm{normal}(0, 1) for m < M and
\qquad \sigma_m \sim \textrm{lognormal}(0, 1) for n < N_m,
then you will have \mu_m \neq \mu_{m'} if m \neq m'.
I’m pretty sure @daniel-saunders-phil meant that each of the \alpha_{m, n} for a fixed m and n < N_m have the same prior (same parameters \mu_m, \sigma_m), which is clear when you write out the math.
[edit: forgot subscripts on N]