Technically the '02+ Explorers use a coil-over design, as a strut is a shock and coil spring mounted together in a coil-over setup that also has the role of locating and guiding the suspension hardware throughout the suspension movement designated to the shock, typically replacing the upper A-arm in an independent suspension setup. A standard coil-over setup, as our Explorers have, only controls ride height and cushions the suspension movement, leaving the suspension hardware locating and guiding to other separate hardware pieces (in our case upper and lower A-arms).
A strut is a simple and common way to refer to what our trucks have, though it is not 100% accurate.
Tom