If a fully loaded (cryogenic fuel + oxidizer) SpaceX rocket did a belly flop into downtown Orlando I suspect this distinction would be quite meaningless to the locals!

Sure but wouldn't most things be meaningless to them at that point? S/he said it was a nitpick, i appreciate the info.

Not sure what exactly are you nitpicking here - ballistic missiles have propulsion for a short time after lunch and afterwards continuing on a ballistic (hence the name) trajectory towards the targets. Cruise missiles have propulsion usually during most of the flight.

A rocket straying off course could either smash into city under full power (thus being a cruise missile) or have its propulsion cut off remotely beforehand (thus being a ballistic missile), depending on a scenario. What kind of a correction were you making?

Cruise missiles are designed to rely on aerodynamic lift (and typically use air-breathing engines, although there have been some "boost-glide" weapons that used rocket engines).

'Cruise missile' has always sounded cooler than ballistic missile, imho. But you are 100% correct according to Wikipedia.