This is a big question and we can only provide very general answers in this FAQ format.
Dark target has separate algorithms for land and ocean. Deep blue in the MODIS aerosol products is a land retrieval only. All total column aerosol retrieval algorithms must account for and remove the surface reflectance signal to accurately determine the aerosol signal. Dark target and deep blue retrievals have different ways of accounting for the reflectance signal coming from the land surface.
Dark target uses a set of ratios and relationships between the 0.47, 0.67 and 2.1 µm channels to account for the surface signal. This method works best over dark vegetated targets and does not work over bright land surfaces.
Deep blue uses maps and libraries of surface reflectance in the blue channels to account for the surface signal as well as spectral reflectance ratios. This method works best over bright land surfaces but can also retrieve aerosols over most vegetated targets.
Additional differences between dark target and deep blue are:
1. Cloud masking methodology.
2. Dark target uses 500 M pixels in its retrieval algorithm. Deep blue uses 1 Km pixels in its retrieval algorithm.
3. In collection 6 dark target has a 3 Km and a 10 Km product. Deep blue has only the 10 Km product.
Additional information from published papers on the dark target retrieval can be found in our reference section.
For more information on the deep blue retrieval please see the following references: