The words "midst", "amid", and "amidst" all mean the same thing, with the one difference that "midst" is a noun, whereas the other two are prepositions (although "midst" has an archaic use as a preposition as well).
I disagree with those who hold that these words are archaic. "Midst" is somewhat archaic as a preposition, but not when used as a noun. It is archaic to say "he is midst the trees". It is not archaic to say "he is in the midst of the trees".
These words are used commonly today by those who exercise an ample vocabulary. If you are learning English, by all means learn these words and use them! They will not make you seem old-fashioned, and everybody understands them. I would even use the archaic prepositon form of "midst" - everyone will understand you and it sounds lovely.
Also, these words are necessary to use because "midst" and "middle" do not mean the same thing. "Middle" is closely related to the concept of "center". "Midst" can also refer to a center (and, historically, that may have been its original meaning) but more commonly it refers to the general area surrounded by something but not necessarily its center. When I hear the word "midst", I never assume it to mean "center".