Calculating distance and angle between two points, C# program
You should avoid using goto statements. Not because it took me a minute to recall what NewPoints : syntax even means, but because goto makes it extremely hard to follow the execution flow. Cases where goto makes code more readable are rare, and yours is not on of those. Just use another while (or do while) loop instead.
Calc is a poor name for a method, because it doesn't say anything about what sort of calculation it performs. It calculates distance you say? Name it CalcDistance then. Oh, wait, it also calculates angle! Maybe CalcDistanceAndAngle then? That doesn't look right... Which is an indication, that you probably need two separate methods: one to calculate angle and one to calculate distance (related to SRP).

var distance = CalcDistance(...);
var angle = CalcAngle(...);

There is a lot of copy-pasting in GetPoints method. You should probably have a method to query single value. For example

static float RequestValue(string message)
{ 
    float value;
    while (true) 
    {
        Console.WriteLine(message);
        Console.SetCursorPosition(14, Console.CursorTop - 1);
        if (float.TryParse(Console.ReadLine(), out value)) break;
        Console.WriteLine("Invalid data has been entered. Try again."); 
    } 
    return value;
}


Then you can just initialize individual points:

var point1X = RequestValue("\nPoint 1\nX Coordinate: ");

I am pretty sure you don't need to move cursor, if you call Console.Write instead of Console.WriteLine.
You are using both floats and doubles in your calculations. You should probably use one or the other.
else return; is unnecessary. 
I think it would make more sense for Calc to take actual points as input instead of "delta"-s. Meaning you should move:


//Getting the change in x and y from point 1 to 2.
deltaX = point2X - point1X;
deltaY = point2Y - point1Y;



inside Calc's body.