Short answer: Yes, there is only a single field whose value varies by position and time.
Long answer: There is only one kind of EM-field, because there is only one gauge boson for the electromagnetic force: the photon. And since photons represent the energy passing through the EM-field, fluctuations in the field propagate at the speed of light.
However, due to the rate of expansion of the universe, some regions of space are moving away from others faster than light. This means that some patches of space are not causally linked—particles in one patch of space can only contribute to the portion of the EM-field "trapped" in that bubble while the rest of the universe expands away.
Regardless, the same laws of physics still hold true in all* patches of space in the universe, so there is still only "one" all-encompassing field. It just means that some components will be forever isolated from others, therefore they cannot interact with each other—through the electromagnetic force or otherwise.
*Actually, modern physics doesn't work if the energy or gravity exceeds a certain point, like in a black hole.