Voltage drop is a generic term for the voltage across a device. Using the word breakdown is more descriptive, but unnecessary. The term drop has never been confined to the forward voltage drop of diodes.
I do understand what you are trying to say - use the more descriptive word if possible, but in many cases, "drop" is the better word, as the voltage drop is exactly the concept you are talking about.
If you are going to get pedantic, all zener diodes above about 6.8V are actually avalanche diodes as the avalanche breakdown process dominates the zener breakdown process. So a high voltage Zener diode is similar to all other common avalanche diodes, except it is manufactured with a precise breakdown voltage. The Zener breakdown only dominates below 4.7V, and in between, both processes are happening at the same time. For convenience, we call both zener and avalanche reference diodes "zener" diodes.
Richard