In the second case, you apply the transformation on the whole sketch.
In the first one, you apply the transformation for the specific matrix inside the pushMatrix.
Thats why

pushMatrix();
      translate(10,-5);
      rect(0,0,10,10);
popMatrix();
pushMatrix();
      translate(10,-5);
      rect(0,0,10,10);
popMatrix();

is different than

translate(10,-5);
rect(0,0,10,10);
translate(10,-5);
rect(0,0,10,10);

You should take a look at : http://processing.org/learning/transform2d/

And is the order right for my assumption for this?

void draw(){
  translate(10,-5);
  rotate(radians(15));
  translate(-10,5);
  rect(0,0,10,10);
}

processing does:
1. translate(-10,5);  2. rotate(radians(15));   3. translate(10,-5);   4. rect(0,0,10,10);

or

1. translate(10,-5);  2. rotate(radians(15));   3. translate(-10,5);   4. rect(0,0,10,10);

It acts in the order of your lines.

But why is it that
pushMatrix()
...
popMatrix()

the result is the same as the one without the push and pop()?


for example:


pushMatrix()
StepA
StepB
StepC
draw()
popMatrix()

the same as

StepA
StepB
StepC
draw()

and i thought that the push and pop works such that StepA gets into the stack and will be the last to come out?
if so, the result explains that the procedure without push and popMatrix will work in Step C first then Step B then followed by Step A.

Could you explain to be why?

In another words, is Processing the same as Opengl which is Post Multiplication for the transformation?

No, you are misunderstanding what pushMatrix() does.
It just saves the current set of transformations (the current coordinate system) in a stack. Then you can add any transformations you want. When calling popMatrix(), the pushed set / system is popped and restored. It is just a means of quickly restoring a given state.