What is the best way to distinguish between those? Is the distinction based solely on ICI (inter-click-interval) and if so, what is the ICI range for a click train versus a burst pulse for example? (<10 ms appears to be the number?)
There is some emphasis on ICI in how burst pulses are defined in the literature. For example, in Lammers et al. (2003) burst pulses described as follows: "Burst pulses were distinguished from echolocation click trains on the basis of their ICIs. Click trains were considered burst pulses if their mean ICI did not exceed 10 ms." (p. 1631).
Similarly, in Martin et al. (2019) burst pulses are defined as follows: "...a discrete, isolated series of high repetition rate clicks produced at a relatively constant rate. " (p. 2) and as " ...isolated series of high repetition rate clicks that generally begin, persist and end with ICIs < 10 ms" (p. 3).
Lammers et al. (2003) also discussed some overlap between burst pulses and terminal buzzes: "Admittedly, this distinction [a burst pulse pattern with interclick intervals consistently less than 10 ms] is not necessarily definitive because click trains are sometimes produced that begin with long interclick intervals ~10–1001 ms and end with very short ones ~1.5–9 ms." (p. 1636).
Lammers, M. O., Au, W. W., & Herzing, D. L. (2003). The broadband social acoustic signaling behavior of spinner and spotted dolphins. The Journal of the Acoustical Society of America, 114(3), 1629-1639.
Martin, M. J., Elwen, S. H., Kassanjee, R., & Gridley, T. (2019). To buzz or burst-pulse? The functional role of Heaviside's dolphin, Cephalorhynchus heavisidii, rapidly pulsed signals. Animal Behaviour, 150, 273-284.