The particle and the wave are nothing more than scientific models.
What is a scientific model? It is a strategy scientists use to understand a certain situation. It may not be entirely correct, but it is still useful in some situations.
The particle is a scientific model where we consider the modeled entity to behave as if it were a "steel ball". It has a negligible geometric size, and it is definitely in one place at one time, and it exists as discrete quantized versions of this entity for which if you split any particle you can no longer consider it to be the entity of interest.
The wave is a scientific model where we consider the modeled entity to exhibit the characteristics of waves known at our macroscopic world, such as interference patterns and diffraction. Waves are more distributed models than the localized particle model.
When considering light to either be a particle or a wave, all we mean is sometimes it is useful to consider it a particle, and sometimes it is useful to consider it a wave. It exhibits both behavior, but never both behavior in the same experiment.
It turns out, all elementary particles behave as both particles and as waves.