From a purely technical point of view, laser engraving and laser etching are completely different laser processes. Laser etching melts the surface whereas laser engraving disintegrates it into dust.
But people who are not laser experts tend to use both terms interchangeably, without making a difference, to refer to any laser process that creates markings on a part (hell, some people even use laser engraving to refer to laser cutting.) The correct term to refer to both processes would be "laser marking", which includes laser etching and laser engraving.
People who use laser engraving and laser etching without knowing the difference may also want to refer to other lesser-known laser processes, but they don't know what those processes are called. For example, laser annealing is another process that creates a chemical reaction under the surface of the material. The surface does not melt, as with laser etching, and is not disintegrated, as with laser engraving. Or, they could also refer to laser ablation, a process that's used when a surface has different layers (for example, a surface is covered with paint). With laser ablation, paint can be removed selectively, without ever affecting the material underneath, to create marks whose contrast is created thanks to the difference between paint and the bare material.
My source is the following website: https://www.laserax.com/laser-marking/etching-engraving