The electron field and the electric field generated by an electron are distinct concepts in physics.
The electron field is a fundamental concept in quantum field theory. According to this theory, particles such as electrons are not considered as discrete objects moving through space but rather as excitations of underlying quantum fields. The electron field permeates all of space, and its quantum fluctuations give rise to electrons and their antiparticles, known as positrons. The electron field is described by a mathematical framework called a quantum field, which assigns a value to each point in space and time.
On the other hand, the electric field generated by an electron is a concept from classical electromagnetism. When an electron is in motion or is at rest but experiencing an external electric field, it generates an electric field in its surroundings. The electric field describes the force experienced by other charged particles in the vicinity of the electron. It is a vector field that has both magnitude and direction at each point in space and is influenced by the presence and motion of charges.
In summary, the electron field is a fundamental field that pervades all of space and is associated with the quantum nature of electrons. The electric field generated by an electron is a classical concept that describes the influence of an electron's presence on other charged particles in its surroundings. While the electron field arises from quantum field theory, the electric field is a concept within classical electromagnetism.