Title is self explaining.
I have never read any piece where the difference between the two made a difference.
encipher |enˈsīfər| verb [ trans. ] convert (a message or piece of text) into a coded form; encrypt.
Well, the semantic difference is that they are different words. One has the ending of ...
I'm going to assume you didn't mean "semantic" but "technical" difference. So the technical difference is, there isn't one. They are the same thing. Only, almost no-one uses the word "encipher". So stick to "encrypt".
In French, there are two words, "chiffrer" and "crypter"; theoretically, the latter would mean "to encrypt but without knowledge of the key, i.e. as part of an attack" (it is more often encountered as "décrypter" which means "to decrypt without prior knowledge of the key"). Relatively few French-speaking programmers are even aware of that distinction, and the French translations of many applications (including Outlook Express) use "crypter" in places where they should use "chiffrer".
In English, I do not think that this distinction actually exists. "Encipher" and "chiffrer" both come from the Arabic "sifr" which means "zero", while "encrypt" and "crypter" come from the Greek "kryptos" (hidden, secret). The use of "sifr" can apparently be traced back to Giovan Battista Bellaso, who published in 1553 cryptographic methods in Latin (as was normal at that time) but with Italian titles such as "La Cifra" and "Novi et singolari modi di cifrare". His point was that his cryptographic techniques involved some computations with numbers, and in 16th century Italy, mathematics were still an import from old Greek by way of Arab writers, brought to the christian Europe during the Crusades. Hence the use of the Arabic root.
In that sense, one could say that "to encipher" means "to encrypt, with some mathematics involved in the process". By definition, this covers any encryption in which a computer was used, so the terms "encipher" and "encrypt" are practically synonymous.