A bit simplified you can think of it as arrays being a special case and not ordinary classes (a bit like primitives, but not). String and all the collections are classes, hence the methods to get size, length or similar things.

I guess the reason at the time of the design was performance. If they created it today they had probably come up with something like array-backed collection classes instead.

If anyone is interested, here is a small snippet of code to illustrate the difference between the two in generated code, first the source:

public class LengthTest {
  public static void main(String[] args) {
    int[] array = {12,1,4};
    String string = "Hoo";
    System.out.println(array.length);
    System.out.println(string.length());
  }
}

Cutting a way the not so important part of the byte code, running javap -c on the class results in the following for the two last lines:

20: getstatic   #3; //Field java/lang/System.out:Ljava/io/PrintStream;
23: aload_1
24: arraylength
25: invokevirtual   #4; //Method java/io/PrintStream.println:(I)V
28: getstatic   #3; //Field java/lang/System.out:Ljava/io/PrintStream;
31: aload_2
32: invokevirtual   #5; //Method java/lang/String.length:()I
35: invokevirtual   #4; //Method java/io/PrintStream.println:(I)V

In the first case (20-25) the code just asks the JVM for the size of the array (in JNI this would have been a call to GetArrayLength()) whereas in the String case (28-35) it needs to do a method call to get the length.

In the mid 1990s, without good JITs and stuff, it would have killed performance totally to only have the java.util.Vector (or something similar) and not a language construct which didn't really behave like a class but was fast. They could of course have masked the property as a method call and handled it in the compiler but I think it would have been even more confusing to have a method on something that isn't a real class.

There are two types of array.

One Dimensional Array

Syntax for default values:

int[] num = new int[5];

Or (less preferred)

int num[] = new int[5];

Syntax with values given (variable/field initialization):

int[] num = {1,2,3,4,5};

Or (less preferred)

int num[] = {1, 2, 3, 4, 5};

Note: For convenience int[] num is preferable because it clearly tells that you are talking here about array. Otherwise no difference. Not at all.

Multidimensional array

Declaration

int[][] num = new int[5][2];

Or

int num[][] = new int[5][2];

Or

int[] num[] = new int[5][2];

Initialization

 num[0][0]=1;
 num[0][1]=2;
 num[1][0]=1;
 num[1][1]=2;
 num[2][0]=1;
 num[2][1]=2;
 num[3][0]=1;
 num[3][1]=2;
 num[4][0]=1;
 num[4][1]=2;

Or

 int[][] num={ {1,2}, {1,2}, {1,2}, {1,2}, {1,2} };

Ragged Array (or Non-rectangular Array)

 int[][] num = new int[5][];
 num[0] = new int[1];
 num[1] = new int[5];
 num[2] = new int[2];
 num[3] = new int[3];

So here we are defining columns explicitly.
Another Way:

int[][] num={ {1}, {1,2}, {1,2,3,4,5}, {1,2}, {1,2,3} };

For Accessing:

for (int i=0; i<(num.length); i++ ) {
    for (int j=0;j<num[i].length;j++)
        System.out.println(num[i][j]);
}

Alternatively:

for (int[] a : num) {
  for (int i : a) {
    System.out.println(i);
  }
}

Ragged arrays are multidimensional arrays.
For explanation see multidimensional array detail at the official java tutorials