Transliteration - The spelling of the words of one language with characters from the alphabet of another. Ideally, this is a character for character replacement so that reverse transliteration into the original script is possible. Transliteration is not concerned with representing the phonetics of the original: it only strives to accurately represent the characters.
Pure transliteration can be quite successful. However, there are dozens of competing, and overlapping transliteration systems to confuse the scholar, who, more often than not feels it his or her place to alter or "improve" on a given transliteration system, often in an attempt to bridge the gap between transliteration and transcription. Add to this the complicated national and international history of transliteration and the frequent ambiguity between the goals of transcription and transliteration by scholars and specialists alike, and the result is a quagmire.
Transcription - The representation of the sound of the words in a language using another alphabet or set of symbols created for that purpose. Transcription is not concerned with representing characters: it strives to give a phonetically (or phonologically) accurate representation of the word. This may differ, depending on the language or set of symbols into which the word is being transcribed.
Because transcription attempts to recreate the meaning-bearing sounds of the original using the alphabet(s) and spelling conventions of the language into which it is transcribed, multiple spellings of the same word are possible for a single language, and dozens may be encountered if searching across languages. Like transliteration, transcription can also be quite successful, as in the IPA system. However, because transcription is most often for the non-specialist, popular systems of transcription tend not to use specialized characters created for the purpose, but rather the alphabets and spelling conventions of the various languages of the non-speakers.