Coffee beans are seeds inside a fruit. Processing prepares those seeds for storage, transport and later roasting by controlling how the surrounding fruit is removed and how the coffee is dried. The words on a bag therefore refer to an earlier part of production, not to a flavoring added to roasted beans.
In a natural or dry process, the cherry is dried with the seed inside before its dried layers are removed. In washed processing, much of the fruit is removed before the coffee is dried. Honey and related approaches retain varying amounts of sticky fruit material during drying; the name does not mean that bees' honey has been added. Actual practices vary by producer, equipment and local conditions, so a broad category cannot describe every operational detail.
Processing can influence fruit character, clarity and texture, but it works together with variety, growing conditions, sorting and roasting. Use the label to form a question rather than to predict a guaranteed taste. Comparing two coffees from the same producer or region, brewed with the same recipe, can make the role of processing easier to explore without confusing every difference with the processing name alone.

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