The two approaches are noted to have close mathematical similarities; The difference between the two is found in their use and interpretation by analysts. Both the component and the ARIMA definition of seasonality emphasize the existence of regular periodic fluctuation; however, unlike the component definition, the ARIMA definition does not emphasize separating this fluctuation from the rest of the time series. Using and interpreting component seasonal analysis is considered, with particular emphasis on the Census X-ll seasonal adjustment program. Further, three kinds of component packages other than the X-ll are also addressed. The X-ll program is shown to be inappropriate for highly irregular series, short series (6 or fewer years), or for series containing an abrupt change or discontinuity. ARIMA methods are also considered: moving average and autoregressive processes are defined, and ways to identify the process of a series are examined. Further, stationarity and differencing are discussed, as is evaluation of ARIMA models. In contrast to the X-ll, which can be used quickly and easily for a large number of series and which has standard options and criteria that can be explicitly stated, ARIMA methods are advised to require a lengthy analysis and reanalysis of each individual series. Thus, ARIMA methods are considered most appropriate for analyzing one or two important series. Included are 21 figures and 134 references.