A simplistic view of the cornice from the three orders would be that Doric cornice is of plainer decoration but with dentils or mutules – thus splitting Doric into denticular or mutular orders; cornice of the ionic order is less complicated in that there are no vertical divisions apart from dentils, but this would have ornamentation such as leaf & tongue; egg & dart; bead and reel; the perpendicular divisions of which correspond to the axes of the dentils, which in turn respond to the axis of the columns.
Cornice of the Corinthian order is similar to the ionic in ornamentation but also has the modillion block incorporated.
Cornice design used in residential property can be seen as having profile design based upon classical entablature with ornamentation based upon the ionic and Corinthian orders. Profiles are set out upon ornamentation integrated with the classical sections comprising of crowning, supporting; binding; separating; and prone details. The most frequently used being the quarter round; cove or cavetto; torus or half round; the cyma; the ogee or cyma reversa and the scotia; the more important mouldings being finished off or separated with fillet sections.
The setting out of the ornamentation to any cornice design is of great importance with special attention required to the pattern and lay out of these ornaments at every miter.
Therefore, whilst some classical cornice designs can be seen as direct forms of the orders, the majority of those used would have only reference to the orders. And would more likely be historically referenced via specific period of architecture such as Georgian; Victorian, regency; or such like.
But even these references can be vague with fluidity of design meaning exact provenance is not always possible.