Right. That's another classic difference between science and engineering ("industry"). Science considers an "omnidirectional" antenna to be
a point source radiating in all directions (isotropic). Industry realizes that an antenna with that radiation pattern has next to zero practical use, so they use the same term to mean that it merely
radiates in all compass directions. It's the reduction (redirection) of the power otherwise wasted in vertical signal that produces the antenna's gain.