Is the term "small" applied differently between piston engine planes and jet engine planes? My understanding was that "small" covered planes up to 12,500 pounds, no matter the engine type.

Would that be gross weight/max takeoff weight?

Brought to mind by the two recent Cessna Citation crashes (Cessna 560, Cessna 680A), and head lines of "Small  jet crashed during takeoff"  and "Small jet crashed during landing". Pretty sure their gross weights, 15900 lbs and 30800 lbs would push them out of the small category.

Luckily, all crew and passengers were able to walk away in both accidents.
I wouldn't expect press headlines to adhere to the FAA or ICAO definitions of "small", "large", "heavy", etc. This would be a public vernacular definition of "small", which would distinguish from the big airliners most people think of when hearing about jet planes.