What does Unit delay function in simulink?

I am trying to compare simulink with raw code.

In this simulation I am trying to understand what the unit delay function does.

https://www.mathworks.com/help/simulink/slref/spiral-galaxy-formation-simulation-using-matlab-function-blocks.html

When I am writing the code on myself (out of simulink) I get different results, even though I have used the same exact equations.

The only difference seems to be the unit delay function. Does it change the equations inside the other functions?