Hi there Emotion: smile Merry X'mas to you all.
I want to ask this "Forget me not" phrase.
Does it has the same meaning as "Don't fore get me" ?
Then, why it used different structure and what is the difference?

I don't believe I've ever heard anybody use "Forget me not" as a sentence -- only the flower "forget-me-not", shown below.

It's an archaic form for the negative mood, mostly used idiomatically now, I guess. It means the same as "don't forget me".

Another famous example is "I like her not!" as said by Henry VIII.

Finally, as a noun, a forget-me-not is a plant.
 CalifJim's reply was promoted to an answer.