Question

What is the difference between the two syntaxes?

Answer 1

The first one is a multi dimensional array while the second is a jagged array. You can take a look at this question to get a description of the diffrerence between the two, but here is an important snippit:

A multidimensional array creates a nice linear memory layout while a
jagged array implies several extra levels of indirection.

Looking up the value jagged[3][6] in a jagged array var jagged = new
int[10][5] works like this: Look up the element at index 3 (which is
an array) and look up the element at index 6 in that array (which is a
value). For each dimension in this case, there’s an additional look up
(this is an expensive memory access pattern).

A multidimensional array is laid out linearly in memory, the actual
value is found by multiplying together the indexes. However, given the
array var mult = new int[10,30] the Length property of that
multidimensional array returns the total number of elements i.e. 10 *
30 = 300.

The Rank property of a jagged array is always 1, but a
multidimensional array can have any rank. The GetLength method of any
array can be used to get the length of each dimension. For the
multidimensional array in this example mult.GetLength(1) returns 30.

Indexing the multidimensional array is faster e.g. given the
multidimensional array in this example mult[1,7] = 30 * 1 + 7 = 37,
get the element at that index 37. This is a better memory access
pattern because only one memory location is involved, which is the
base address of the array.

A multidimensional array therefore allocates a continuous memory
block, while a jagged array does not have to be square like. e.g.
jagged1.Length does not have to equal jagged[2].Length which would
be true for any multidimensional array.

Update:

One major difference between the multi and jagged array is that a multi must always be “square”, meaning that any two indexes will have the same number of elements in their child arrays. A jagged array does not have this requirement. Take a look at the code below:

var jagged = new int[3][]; //not defining the size of the child array...
var multi = new int[3,8]; //defining a 3x8 "square"
var multiBad = new int[3,]; //Syntax error!
var jaggedSquare= new int[3][8]; //another 3x8 "square"