The most well-known traditional Greek grape marc distillate made from winemaking pomace is called “Tsipouro”. Its production involves various grape pomace cultivars, preparation protocols, and anise-flavoring or not, and it should be a colorless liquid with intense organoleptic properties due to the raw materials used in its production and have a minimum alcoholic strength of 37.5% by volume. This study aimed to characterize the volatilome of tsipouro products by covering as many geographical areas and production styles as possible, as there is a lack of characterization of the aromatic composition of this Greek traditional alcoholic beverage. A Headspace Solid Phase Microextraction Gas Chromatography–Mass Spectrometry (HS-SPME-GC-MS) method was applied in 60 samples, resulting in the identification and semi-quantification of over 90 volatile compounds. The statistical analysis pointed out the metabolites that characterized each traditional product group and underlined the influence of the geographical origin and the production protocol. Aniseed spirits from Northern Greece, Macedonia, Limnos Island, and Thessaly, produced from Muscat pomaces, were found to be richer in terpenes, terpenoids, and flavored compounds, attributing to product aroma and quality; different terpenoids were found to be dominant in Muscat distillates from different regions, showing the importance of geographical origin and production process. In conclusion, the results demonstrated the high aroma variability of the Greek Tsipouro, explained that this diversity is caused mainly by the raw material, and could be helpful in the better protection of the origin of this traditional product and the improvement of its quality.