What is the semantic difference between "encipher" and "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 the 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 was still an import from old Greek by way of Arab writers, brought to 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.
There are a number of differences depending on context:
In cryptology encipher and encrypt are synonymous. There was an effort a few years ago to stop using the root word crypt and use the root cipher instead because some cultures associate the root crypt with death (tales from the crypt). Hence encrypt = to kill. This change never really caught on. In terms of use certain uses of the words are preferred to others. For example: "one 'encrypts' plaintext with a cipher", rather than "one 'enciphers' plaintext with an 'encryption'".
Outside of cryptology decipherment refers to decoding or understanding codes and languages that are not designed to keep secrets but are unknown. For example determining the genetic code or figuring out how to translate mayan.
The answer that Justice gave is incorrect:
"If one 'enciphers,' then one is using reversible cryptography. If one 'encrypts,' then one might be using either reversible cryptography or irreversible cryptography".
While cryptology contains reversible function and non-reversible 'one-way' functions, the term encryption/decryption explicitly refers only to reversible functions.
"In cryptography, encryption is the process of transforming information (referred to as plaintext) using an algorithm (called cipher) to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key." - http://en.wikipedia.org/wiki/Encryption