What does Unit delay function in simulink?

4 Gen 2021
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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?

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