An ESRI GRID can have several columns in its value attribute table (VAT). When performing an Identify on a raster in ArcMap, which is using a Stretched renderer, the Identify window returns the value of the pixel, its stretched value, and the attribute information. However if there are more than 256 unique values, the attribute information is not shown.
By design, the Identify tool returns true pixel values as well as values after rendering, which translates to what is displayed on the map. ArcMap displays a raster, which has a table of more than 256 values, with a Stretched renderer by default, and Identify returns a pixel value and stretched value.
To identify all the attribute information in the table, change the renderer to a unique value renderer before performing an Identify. Refer to ArcMap: Drawing thematic raster datasets representing unique categories for more information.