Are there differences between initializing at start and at declaration part

 private Rigidbody rb { get { return GetComponent (); } set { rb = value; } } 

The above statement is called a "Property"

This one in particular is written incorrectly. It's called rb

Notice what will happen when you try to assign rb a value:

rb becomes equal to a value, - but oh wait, rb is a property, so let's invoke "set" on it. Fine, rb becomes equal to a value, - but oh wait, rb is a property, so let's invoke "set" on it.... This results in a recursion.

The correct way to do this would be

 private Rigidbody myPrivateRigidbody = null;//notice, private.
 public Rigidbody rb {get{return myPrivateRigidbody;} } //notice, no set here, and it's public.
 
 void Start(){
 //we can access our private variable, others will have to use property, which only has getter
     myPrivateRigidbody = null; 
 }

Basically, set allows you to assign the incoming value to anything that was declared before (never to a member variable itself, as shown in the above example)

get does the opposite. Get fetches the value from somewhere, then provides it, similar to how a function would.

So they are pretty much like Rigidbody getSomeValue(){return myPrivateRB;}or void setSomeValue(Rigidbody value){myPrivateRB = value};

As you can see, properties are very much like functions, but can be used like normal variables, without the () brackets