Yes, it should be the correct Version to the one shown, however what you might be thinking of is the character. Usually on the Instruction Booklet, the character in the demonstrations looks a bit like this or this .
But you can get many different characters - you're not stuck with one!
If you mean the colour theme, there are so many that there can't be a seperate Instruction Booklet for each one! Probably somewhere it says "exact colour and design may vary from one shown on pack", which means that the Tamagotchi might be a different colour to the one shown in the Instruction Manual.
Here is a link to all the characters you can get on your tamagotchi.
I have a interesting thing to tell you. When I first got my silver and black tamagotchi I got the exact same chain that was shown in the instruction booklet and so did my friend. But when I got my white and pink tamagotchi it didn't follow it so don't worry!