My question is: Is the code equal with or without shield version?
That depends on how you connect your LCD to your Arduino. You must make sure that the numbers in the LiquidCrystal lcd (x, x, x, x, x, x) statement match the connections between your LCD and your Arduino.
It would have been a lot clearer if the perpetrators of the tutorial had included at least a few more comments:
//LiquidCrystal lcd(RS, E, D4, D5, D6, D7);
LiquidCrystal lcd(7, 8, 9, 10, 11, 12); // put your pin numbers here
In the example above the LCD RS pin goes to the Arduino D7 pin, The LCD E pin goes to the Arduino D8 pin, etc.
//LiquidCrystal lcd(RS, E, D4, D5, D6, D7);
LiquidCrystal lcd(8, 9, 4, 5, 6, 7); // put your pin numbers here
On your shield the LCD RS pin goes to the Arduino D8 pin, the LCD E pin goes to the Arduino D9 pin, etc.
//LiquidCrystal lcd(RS, E, D4, D5, D6, D7);
LiquidCrystal lcd(12, 11, 5, 4, 3, 2); // put your pin numbers here
In the tutorial the LCD RS pin goes to he Arduino D12 pin, the LCD E pin goes to the Arduino D11 pin, etc.
It really doesn't matter which Arduino pins you use as long as the connections and the LiquidCrystal led() contents match. This means that you can use the same code with and without the shield if your LCD to Arduino connections match those on the shield.
It is much easier, however, to connect the wires so they are easy to follow or so they do not conflict with other devices you have connected to the Arduino, and adjust the code to match. This is essentially what they did when they designed the pc board for the shield.
So i looked into the potentiometer i have and it says: W-50K 8009ER... instrutions say it must be a 10K, could this be the problem ??
That is a 50K potentiometer and it should work correctly as long as you have connected it correctly. With just the backlight, the power, and the potentiometer connected (LCD pins 1, 2, 3, 15, and 16) you should be able to see blocks on the LCD with the potentiometer at one end and a blank screen with it set at the other end. The correct setting is when you can just barely see a line of blocks on the top row.