The electron is a quantum mechanical entity.
This means that it is constrained to follow the solution of a quantum mechanical equation . This solution is called a wavefunction because it has a sinusoidal dependence .
The wavefunction does not describe a path for the electron, but when complex conjugate squared it gives the probability of measuring the position of the electron at an (x,y,z,t). Thus it is the probability that waves, not the electron.
The double slit experiment one electron at a time, shows the dots which are the electron as it appears macroscopically, and its probability distribution as a wave interference.
The spiral in this bubble chamber picture is an electron kicked out of a hydrogen atom. It leaves a particle path, which follows the classical equations for a particle loosing energy in a magnetic field.
The rule of thumb to know when a particle appears in its probabilistic aspect, i.e. it is necessary to describe it quantum mechanically, is the Heisenberg uncertainty principle (HUP). If the momentum and location determination are within the HUP bounds it is necessary to use the quantum mechanical solution. In this case if one substitutes the numbers , the electron track is way outside the HUP constraints.