Within a GIS data is displayed on one of three formats: points, lines or polygons. How that data is represented depends on the attribute data which is linked to the spatial elements. For example, points could represent cities. If we only have the names of the cities we would class this data as nominal as we only have the names. If we have non numerical data which also describes the size of the city then this could be shown as an interval class where data is represent by for example, small, medium and large depending on population size. Information about the population size of the cities which would enable us to additionally represent the points as numeric values would be termed an ordinal data class.
With a paper map all the information is contained within a single sheet of paper. This information may tell you all you need to know about some basic features of the map. However, if you want to carry out more specific tasks involving spatial queries and analysis the paper map has many limitations.
Firstly, to avoid the original map from being marked the answer is to use some form of overlay such as a plastic sheet. With this technique you are able to put points, lines and polygons on the map without effecting the original. Whilst this is one way of using a map to analyse data it is far from satisfactory. This is where a GIS system is far more effective. With a GIS you can have a base map similar to a paper map and then add as many layers as needed to this to create the analysis you require.If you were a local authority you may want to have layers for lamp posts which would be represented by a points layer, land boundaries which would be represented by polygons or roads which would be represented by line layers. The same base map would be used by different departmental users for completely different applications without the problems normally associated with paper maps.
Joe Short BSc has been involved with various mapping solutions since 1993. If you are considering implementing a GIS or have ArcGIS, MapInfo or Quantum GIS training requirements I would be happy to be of assistance to your organisation.