The moving average model specifies that the output variable depends linearly on the current and various past values of a stochastic (imperfectly predictable) term. Rather than using the past values of the forecast variable in a regression, a moving average model uses past forecast errors in a regression-like model.
The primary difference between an AR and MA model is based on the correlation between time series objects at different time points. The covariance between x(t) and x(t-n) is zero for MA models. However, the correlation of x(t) and x(t-n) gradually declines with n becoming larger in the AR model.
This means that the moving average(MA) model does not uses the past forecasts to predict the future values whereas it uses the errors from the past forecasts. While, the autoregressive model(AR) uses the past forecasts to predict future values.
As mentioned earlier, the MA model, instead of depending on the previous forecasts like in AR model, depends on the error of previous forecasts. Hence the noise quickly vanishes with time in MA model.
Hope this helps!!