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.
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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on 4 Jan 2021

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