the difference between a 'classical' electron and what modern physics calls a 'naked' electron has to do with quantum theory.
The quantum foam depicted at the smallest scale contains large numbers of electron-positron pairs which are produced, live extremely short time, then annihilate again. In the absence of a charged particle, the magnetic and electric fields associated with them are in random directions so they cancel out over larger distances. But a 'real' electron's electromagnetic field polarizes the cloud of electron-positron 'virtual' particles in it's vicinity by attracting the positrons and repelling the electrons. seen from a slight distance, it appears the 'real' electron has taken on some size, as the outer cloud of 'virtual' electrons is negatively charged and the whole ensemble will act like a negatively charged, spatially extended (ie large - for an electron, anyway) object for most interactions at normal energies. The charge will be slightly dampened from a distance, some of the 'real' electron's charge is consumed in polarizing the 'vacuum'.
With the advent of modern high-energy particle accelerators, physicists are able to conduct experiments at high enough energy that the 'naked' electron's properties can be measured. The charge of a 'naked' electron is slightly greater than a 'classical' electron, since it's not being covered up by a cloud of virtual particles. But the size is much much smaller. In fact, as far as we can tell, a naked electron is a pointlike object.
hope that helps some. . .. if you're still reading, read on! .. .
A Note on the quantum foam and particle pair formation:->
due to heisenberg's uncertainty principle, particles can spontaneously arise if they don't live long enough to be detected. (if they coudn't, then we would know their exact position and momentum to be exactly zero, and exact knowledge of both of these at the same time is prohibited by heisenberg's.) But the bigger the particle, the shorter a lifespan it can have in it's 'virtual', i.e. undetectable, existence. however, for particles as small as an electron, they can stick around just long enough to have a noticable effect on normal 'real' particles. but the point is that what had been considered classically as a vacuum is actually inhabited by many many short-lived particle pairs, such as electron-positron. since the energy at any point in space can't be exactly zero, sometimes the residual energy manifests in the production of electron-positron pairs (in theory any particle-antiparticle pairs are allowed, but electron-positron pairs are the ones we will consider
