Isn't that just the change between rad/s and Hz?

It’s more precisely the difference between “rationalized” and “unrationalized” units.

You need a factor 4pi in either Gauss’ law or Coulomb’s law (because they are related by the area 4pi*r^2 of a sphere), and different unit systems picked different ones.

It’s more akin to how you need a factor 2pi in either the forward or backward Fourier transform and different fields picked different conventions.

> It’s more akin to how you need a factor 2pi in either the forward or backward Fourier transform and different fields picked different conventions.

Some fields even use the unitary transform -- they split the difference and just throw in a 1/sqrt(2pi) in both directions.

https://en.wikipedia.org/wiki/Fourier_transform#Angular_freq...

It is more involving [1]

[1] https://phys.libretexts.org/Bookshelves/Electricity_and_Magn...