metric: The metric framework is the most common for humans and considers a two-dimensional space in which it places the objects. The objects are placed with precise coordinates. This representation is very useful, but is sensitive to noise and it is difficult to calculate the distances precisely.
topological: The topological framework only considers places and relations between them. Often, the distances between places are stored. The map is then a graph, in which the nodes corresponds to places and arcs correspond to the paths.
Voronoi diagram
Grid
Advantages of topological maps:
Only sparse data storage
Representation matches problem description: e.g.
instruct robot to move between discrete locations
Recognition only requires consistency, not accuracy