Ilford published ID-3 in two forms, as a single solution, and as a two part developer, The two part just separates the Carbonate into Part B which greatly improves keeping properties. In use, once dilute/mixed, there is no difference at all.
In the DCB 3 & 4 ID-3 is listed as a Soft Working developer. It's a developer I usually have on the shelf in the 2 part form, for two bath print development. It is not a Divided developer.
Kodak D165 is virtually identical to ID-3 both are film and paper developers.
Ian