When I studied Hebrew our teacher (a very old and precise man) told us to transcribe something and was flabbergasted when he found we had all transliterated it. To him the difference must have seemed obvious.

Transliterate = render letter by letter, so that you can tell what the spelling in the original script was.

Transcribe = render the actual pronunciation of.

An example might be Japanese zyuuzitu (t/lit), jujitsu (t/scr).