As this discussion has unfolded, I've found myself becoming less agnostic about the terminology. My preference is for "band beam". Here's why:
1) I found neither "continuous drop" nor "band beam" in my ACI terminology document. So no silver bullet there.
2) In my opinion, the that stuff we choose to show on our slab drawings should be 95% about clearly communicating intent to our contractor friends. Structural designers can, and should, fend for themselves.
3) Viewed in plan, an continuous drop sure does look like a wide beam.
4) In my market, a continuous drop will often have stirrup shear reinforcement, much like a beam and not like a drop panel.
5) In my market, a continuous drop will often have continuous, column to column top steel, much like a beam and not like a drop panel.
6) In my market, a continuous drop will often have concentrated, large diameter bottom steel running column to column, much like a beam and not like a drop panel.
In summmary, when a contractor is reading my plans and trying to identify all of their beams for pricing and planning, I like that continuous drops present like beams as that will alert the contractor to all of the beam-like features that will need to be installed in the continuous drops.