While Holt-Winters method belongs to the family of exponential smoothing based on a description of the trend and seasonality in the data, ARIMA models aim to describe the autocorrelations in the data. Arguably Holt-Winters may be considered a subset of the ARIMA models when seasonality components are accounted for but ARIMA can incorporate independent regressors which H-W cannot. There are other similarities and also differences between the two methods. I recommend checking out the (freely available online) book: Forecasting, Principles and Practice, by Rob Hyndman and George Athanasopoulos.
