Casual scripts are often called informal scripts. Brush scripts are usually part of this category but here they have been separated out. What is left are informal scripts that are derived from lettering or writing made with other tools: broad pens (ITC Humana Script), pointed pens (Memoir), ball-point pens (Caflisch Script), felt tip markers (Longhand), pencils (Graphite), ruling pens (Musclehead), spray cans, etc. Casual scripts have more bounce and irregularity of rhythm than formal scripts. Many have roughened edges, even ink splotches (e.g. Smack). OpenType casual scripts have large glyph sets that make newer designs more successfully substitute for actual handwriting.
Some casual scripts are really casual or informal lettering (such as Tisdall Script or Hatmaker) that come from handlettering. The letters do not join up or even make a pretense of doing so. But they are clearly outside of the history of regular type and thus placed in this category.