Why does the class that implments an interface becomes a child class pf that interface?

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Java

code :
public class A extends B
or

public class A implments B (interface) 

I can understand about the comman concept that why a class when inherits or extends to other class become a child class of their inhereted class.

But...why does an class that implements an interface become a child class of that interface ?

why can i cast the class object with the reference of the interface ?

What I have tried:

i tried google , but didnt got any indeth information