Do these 2 codes mean the exact same thing?

Questions & Answers
1

var grounded : boolean = false;
var groundCheck : Transform;
var groundRadius : float = 0.2;
var whatIsGround : LayerMask;

function Awake()
{
	groundCheck = transform.Find("groundCheck");
}
//Only Update changes in both scripts.
function Update()
{
    grounded = Physics2D.OverlapCircle(groundCheck.position, groundRadius, whatIsGround);
}

or replace the Update part with

if(Physics2D.OverlapCircle(groundCheck.position, groundRadius, whatIsGround);)
{
   grounded = true;
}
2

Yes, they will function identically. The second one is just a bit redundant.

3

if( Physics2D.OverlapCircle(groundCheck.position, groundRadius, whatIsGround) != null)
{
grounded = true;
}
As mentioned in the documentation for Physics2D.OverlapCircle, this returns a collider and hence allocates memory, so if you just need to know how many objects are colliding with the sphere, you may wanna use Physics2d.OverlapCircleNonAlloc

out Collider2D[] results;
if( Physics2D. OverlapCircleNonAlloc(groundCheck.position, groundRadius, results, whatIsGround) > 0)
{
  grounded = true;
}