  Advances in the generation and the application of spatiotemporal optical
vortices (STOV) are proceeding fast, but fundamental aspects of their nature
remain obscure. Phys. Rev. A 107, L031501 (2023) (PRA) and Prog. Electromagn.
Res. 177, 95 (2023) (PIER) provide contradictory results on the transverse
orbital angular momentum (OAM) carried by STOVs. We show that the results by
Porras in PIER and by Bliokh in PRA refer to different STOVs and are all
correct. In PIER, STOVs are elliptical at given cross section and time, or in
space-time, but not in three-dimensional space. In PRA, STOVs are elliptical in
space but not in space-time. This is evidenced from two dual, equivalent
theories on the transverse OAM where a wave packet is seen in space-time
evolving with propagation distance or in space evolving in time, that accounts
for all values of the total, intrinsic and extrinsic OAM in PIERS and PRA.
However, the intrinsic OAM with respect to the photon wave function center in
PRA is not generally conserved, which advocates for the energy center in PIER
as the STOV center. We argue that STOVs are generated in experiments to
purportedly have elliptical symmetry in space-time. The values provided in PIER
should then be taken as the reference for elliptical STOVs, and the theory
therein to evaluate the transverse OAM of other wave packets. Hancock et al. in
Phys. Rev. Lett. 127, 193901 (2021) and Phys. Rev. X. 14, 011031 (2024)
erroneously attribute the transverse OAM of elliptical STOVs in space to the
elliptical STOVs in space-time they consider theoretically and can generate in
their experiments.
