For simple exponential smoothing, \begin{align*} y_t &= \ell_{t-1} + e_t \\\\ \ell_t &= \ell_{t-1} + \alpha e_t \end{align*} So the forecast of $y_{t+1|t}$ is also a forecast of $\ell_{t+1|t}$. That is, both conditional distributions have the same mean, and the forecast is an estimate of that mean.

Everything you want to predict has a random component, otherwise you would know its value and there would be no need to predict it. Forecasts are just estimates of the means of conditional distributions.

For simple exponential smoothing, \begin{align*} y_t &= \ell_{t-1} + e_t \\\\ \ell_t &= \ell_{t-1} + \alpha e_t, \end{align*} where $e_t$ is a white noise error. So the forecast of $y_{t+1|t}$ is also a forecast of $\ell_{t+1|t}$. That is, both conditional distributions have the same mean, and the forecast is an estimate of that mean.

Everything you want to predict has a random component, otherwise you would know its value and there would be no need to predict it. Forecasts are just estimates of the means of conditional distributions.