This problem is called ‘lost motion’. A motion is commanded by the controller but it does not arrive in the finished product.
I believe that your second picture demonstrates the problem nicely.
The light text on a dark background is done by engraving the background by sweeping back and forth. Your engraver does not stop and start and follow the letters.
Stopping and starting ( accelerating and decelerating ) too quickly can cause lost motion - but with letters the missing motions are small (and within the letter) while the laser is engraving. This makes it very difficult to see. The errors accumulate but can average out to zero or stack up in a particular direction.
The cure in this instance is to slow down and reduce power. If time allowed I would repeat the task and choose half the engrave speed and half the engrave power (to keep the engraving effect the same) to prove that was the issue - then speed up as the circumstances allowed.
Loose components in an engraver can also cause lost motion. The changes here are subtle and not a large loss like the loss caused by a belt slipping. Recheck the set screws that secure the shafts, cogs and couplers. This can can be the other source of lost motion.
If slowing doesn’t fix the problem, and if the screws are all tight I would consider this as a third possibility.