I am a bit confused, as during my studies I learnt that rasters have
only one cell value and for some it might be true, as the attribute
table is greyed out in ArcGIS. But for others, multiple fields are
provided, so the assumption seems to be wrong.
I had similar questions about Raster Attribute Table (RAT)s
What is a raster attribute table?.
I think one cause of the confusion is that the raster attribute table for a raster is not really an "attribute table" in the sense of attributes in the vector data model. In the vector model, the attributes are for each individual object/row. So if you have 100 geometric elements in your vector layer, you will have 100 rows in the attribute table.
In contrast, in RATs, you don't have a record (set of attribute) for each pixel/cell. (And indeed, people don't/can't typically store very complex attributes for each pixel.) Instead, you have a record for each cell value. So if you have 100 pixels in a binary (0/1) raster/image, you will have 2 rows for each value. (If the "attribute" in the RAT is a count of pixels of a particular value, e.g. 0 or 1, your RAT is really just a histogram of the image, which is a summary of the pixels.) This is probably why RATs are also called Value Attribute Tables (VAT), which is a much less confusing name IMO.