All datasets in GIS can be categorized as being either discrete or continuous.
What is Discrete GIS Data?
Discrete data is geographic data that only occurs in specific locations. For polygon data, discrete data has well defined boundaries. Point and line GIS data such as tree locations, rivers, and streets all fall into the category of discrete datasets. Maps made with discrete GIS data will have areas on the map that contain values from that dataset and areas on the map where that dataset is absent. In this map example below, tornado locations (red points) are an example of a discrete GIS dataset.
What is Continuous GIS Data?
Continuous data has no clearly defined boundaries. Every point on a map made with continuous GIS data will contain a value. Elevation, slope, temperature, and precipitation are examples of datasets that are continuous. In the example map below, every point on the map within the contiguous United States contains a temperature value.