Yes, Mapnik is yet another WMS/WMTS server which specializes in rendering OSM or GDAL/OGR data as fast and beautiful tiles.
Mapserver and Geoserver also have their own renderers, and their own
cache tile systems (Mapcache, GeoWebCache). They are also implementing
other OGC standards like WFS. As far as i know Mapnik does not support
such a standard and is not planning to. Of course, the Mapnik folks can
probably explain main features and differences much better than me.
Another minor difference is that Mapnik isn't an OSGeo project, compared to the two other servers you mentionned.