As far as I'm aware of, transition time is sometimes used as a collective term for both rise- and falltime, but has no specific meaning besides them. If rise- and falltime are applied to digital signals, they don't exactly mean small signal.
The important point is however to distinguish betweeen small signal rise- and falltime and large signal slewing time (respectively slew rate) of an amplifier, as mentioned in post #3.
In high speed OP data sheets, you sometimes find rise- and falltime specified for large signal, which is strictly spoken a combination of small signal circuit speed and slew rate. This corresponds to the fact, that these quanties can be measured e.g with an oscilloscope, that doesn't care about small or large signal.