Let us denote the implied vol on day $t$ for absolute strike $K$ and maturity tenor $T$ as
$$\sigma_t(K,T)$$
If $S_t$ denotes the spot value on day $t$ then $\sigma_t(S_t,T)$ is referred to as At-The-Money (ATM) vol.
(Note: I'll ignore things like ATMF here)
If we assume sticky-strike (i.e. any option's implied vol doesn't move in absolute strike-terms when spot moves), then for any fixed strike $K$ and maturity tenor $T$ a scenario move could be
$$s_t(K,T) = \sigma_t(K,T) - \sigma_{t-1}(K,T)$$
and if $\sigma_{today}(K,T)$ is today's value then the simulated vol scenario value could be
$$\sigma_{sim_t}(K,T) = \sigma_{today}(K,T) + s_t(K,T)$$
Now, the problem is that you cannot record moves $s_t(K,T)$ for all possible $K,T$. I mean, where does it end? So one example of a simpler approach is to look at parallel vol moves (one per maturity), which we could proxy via the ATM vol.
Since we are assuming sticky-strike we cannot use
$$\text{ATMVol}_{t} - \text{ATMVol}_{t-1} = \sigma_t(S_t,T)
- \sigma_{t-1}(S_{t-1},T)$$
as a valid vol move, because in general $S_t\ne S_{t-1}$. The correct move to look at is
$$s_t(T) = \sigma_t(S_t,T) - \sigma_{t-1}(S_{t},T)$$
Note the subtle difference in subscripts: $S_{t-1}\to S_{t}$. Then a simulated vol scenario could be
$$\sigma_{sim_t}(K,T) = \sigma_{today}(K,T) + s_t(T)$$