The following paragraph is excerpted from Brockwell, Davis: Time series: theory and application, section 13.2:
An ARMA process $\{X_t\}$ is often referred to as a short memory process since
the covariance (or dependence) between $X_1$ and $X_{1+k}$ decreases rapidly as
$k \to \infty$. In fact we know from Chapter 3 that the autocorrelation function is
geometrically bounded, i.e.
$$\left|\rho(k)\right| \leq Cr^k \quad k = 1, 2, ... $$
where $C > 0$ and $0 < r < 1$. A long memory process is a stationary process
for which
$$\rho(k) \sim Ck^{2d-1} \text{ as } k \to \infty$$
where $C \neq 0$ and $d < .5$.
Intuitively, the "short memory (or term, in your words)" and "long memory" time series correspond to the correlation between two observations with lag $k$ are "small" (with geometric decreasing order) and "large" (with power function order, but is still decreasing to zero slowly), respectively.
Consequently, a short/long term forecasting is the forecasting for which the underlying time series model is short/long memory time series.