  Motivated by recent progress in the generation of optical spatiotemporal
vortex pulses (STVPs), there is a theoretical discussion about the transverse
orbital angular momentum (OAM) carried by such pulses. Two recent works [K. Y.
Bliokh, Phys. Rev. Lett. 126, 243601 (2021)] and [S. W. Hancock et al., Phys.
Rev. Lett. 127, 193901 (2021)] claimed the OAM values which differ by a factor
of 2 for circular STVPs. Here we resolve this controversy by showing that the
result by Hancock et al. is correct for the total OAM, while the result by
Bliokh describes the suitably defined intrinsic part of the OAM. The other,
extrinsic part of the OAM originates from the fact that plane waves of the same
amplitude but different frequencies in the pulse spectrum contain different
densities of photons, which induces a transverse vortex-dependent shift of the
photon centroid even in a STVP with symmetric energy-density distribution. We
describe similar peculiarities of acoustic and quantum-relativistic
(Klein-Gordon and arbitrary-spin) STVPs. In all cases, only the intrinsic OAM
keeps a universal form independent of the details of the problem and similar to
the OAM of monochromatic vortex beams.
