OK, that is kind of technical, so let me try to clarify. An electric charge at rest will interact differently with the x- and y-components of an electric field (the Ex will cause an acceleration in the x-direction, Ey in the y-direction). The full field may be roughly thought of as having six components and an electric charge will respond differently to all six. And, they are all mixed up depending on your motion. If you have a pure electric field but observe it from a frame moving by it, magnetic fields emerge like magic.