What is the difference between these two methods and when would you use one instead of the other?

int[,] array = new int[4,3];
int length0 = array.GetLength(0);
int upperbound0 = array.GetUpperBound(0);

MSDN says that GetLength return the number of elements where as GetUpperBound determine the max index, but how could this be different since arrays are initialized with elements for each index?

Take a look at this (rarely used) method. From Docs:

public static Array CreateInstance(Type elementType, int[] lengths, int[] lowerBounds)

Creates a multidimensional Array of the specified Type and dimension lengths, with the specified lower bounds.

With it, you can create an array with indices from -5 ... +5. If you ever use this kind of array, then GetUpperBound() suddenly becomes a lot more useful than GetLength()-1. There also exists a GetLowerBound().

But the C# support for this kind of arrays is low, you cannot use []. You would only need those methods in combination with the Array.GetValue() and SetValue() methods.

I realise this is an old question but I think it's worth emphasising that GetUpperBound returns the upper boundary of the specified dimension. This is important for a multidimensional array as in that case the two functions are not equivalent.

// Given a simple two dimensional array
private static readonly int[,] USHolidays =
{
    { 1, 1 },
    { 7, 4 },
    { 12, 24 },
    { 12, 25 }
};

The Length property will output 8 as there are 8 elements in the array.

Console.WriteLine(USHolidays.Length);

However, the GetUpperBound() function will output 3 as the upper boundary of the first dimension is 3. In other words I can loop over array indexes 0, 1, 2 and 3.

Console.WriteLine(USHolidays.GetUpperBound(0));
for (var i = 0; i <= USHolidays.GetUpperBound(0); i++)
{
    Console.WriteLine("{0}, {1}", USHolidays[i, 0], USHolidays[i, 1]);
}