You can't have a feature class of point, line, or polygon without also having an attribute table. "Fields" is something that is common to all of those and thus they have a shared UI. Raster data on the other hand, does not always have a table. Multiband imagery doesn't support tables, nor does 32 bit float. Integer data can support a table, but depending on the data it may be built automatically or it could be up to you to run the Build Raster Attribute Table tool to force a table to be built. Because of the lack of uniformity among the various types of raster data with respect to attribute tables, they do not have a shared "Fields" tab in the properties dialog.