Dendritic Drainage System, has a branching/ tree-like drainage pattern, develop in areas of uniform rock, with little distortion by folding or faulting. The rock (or unconsolidated material) beneath the stream has no particular fabric or structure and can be eroded equally easily in all directions.
Deranged drainage system is an irregular broken drainage system, where there is no coherent pattern to the rivers and lakes. It happens in areas where there has been much geological disruption. Rivers have not had time to adapt to the underlying rock structure, and follow the irregularities of glacial deposits.
EDIT: Adding Arc Hydro: Overview of Terrain Preprocessing Workflows , as referred by Dean.
From the point of view of DEM processing, dendritic terrains do not have sinks/depressions while deranged terrains do. Specifically with Arc Hydro tools, dendritic terrains have only streams (no sinks), deranged terrains have only sinks (no streams), and combined terrains have both. There are different workflows and tools to use for processing these three terrain types. Please review the details in Arc Hydro document "Arc Hydro - Overview of Terrain Preprocessing Workflows".