[Timo]

This isn't an official answer, merely a personal opinion.

To me, an "impulse" implies a controlled and expected occurence, which has a rise and a fall in the signal. An impulse only happens once. Several/Multiples would be "impulses".

To me, a "transient" is a description of the leading edge of a signal that has changed extremely suddenly, from rest. Like an initial, very abrupt change in the audio waveform on the leading edge of a kick drum, for example.

I guess both terms are interchangable to an extent.

The term "Transient" is used a lot in electric current or electronic areas of study (to describe a brief but very powerful power-surge, or the like), or to describe very sudden changes.