Electrons are massive spin-1/2 quanta and thus have some particle properties, e.g., they are localizable to a certain extent. Of course as elementary particles they are neither classical particles nor classical fields but described by a quantized Dirac field. Under some circumstances the probability distribution for finding an electron at a given point on a screen shows the same pattern as classical wave intensities predict, but the interpretation is completely different: Quantum theory is inherently probabilistic, i.e., the electron cannot be interpreted as an extended object like a classical (e.g., electromagnetic) field, but its wave function (which makes sense in the non-relativistic limit) provides the probability distribution for its position, i.e., letting an electron run through a double slit will always yield in its detection in one point-like region (of finite extent however!), but the very position each individual electron ends up cannot be predicted better than with the probabilities provided by the wave function, which can be calculated with help of Schrödinger's Equation. Letting run very many electrons through the slits, always prepared in the same way, yields a distribution on the screen which looks like the interference pattern of corresponding waves, but note again, modern quantum theory has been discovered, because the old-fashioned quantum theory a la Planck, Einstein, Bohr, and Sommerfeld was inconsistent in itself and also quantitatively wrong in even quite simple cases (like for the predicted spectra of all atoms except the hydrogen atom). Thanks to Born, Jordan, and Heisenberg, Schrödinger, and particularly Dirac in 1925/26 we have modern quantum theory today, which is the most successful theory ever, and there's no wave-particle dualism and likewise self-contradictory features of the old theory.
Now let's briefly come to photons. It's unfortunate that most popular books on QT start with photons, providing wrong pictures about them, even more than 80 years after the correct description of them by Dirac. Even introductory university textbooks provide still wrong pictures in their introductory chapters. Photons are, however, among the more difficult subjects to explain and cannot be understood without the full use of relativistic quantum field theory. Forget about any particle picture you might have been suggested by such bad popular-science writing! It's very probable to be wrong or at least misleading. First of all it's a mathematical fact that photons, as we understand them within the most accurate theory ever, the Standard Model of elementary particles, are not localizable in any sense. It's not even possible to define what the position observable of a photon might be. The only thing you can define and measure are detection probabilities for a given experimental setup. In the case of the double-slit experiment with single photons the description of these probabilities is not much different from that for electrons, and you get probability distributions as predicted by classical electrodynamics, but again particularly what's nowadays understood as a "single photon" is far from being anything classical. It's not a bullet-like particle since it's not even posssible to define its position nor is it in any sense localizable, but it's also not like a classical electromagnetic wave field either. E.g., the expectation value for the lectromagnetic field ##(\vec{E},\vec{B})## of the single-photon state vanishes. On the other hand a photon carries energy, momentum, and angular momentum. As I said before, you cannot understand what a single-photon state is without studying relativistic quantum field theory and quantum electrodynamics.
