For example, I translate a word from English to German. I call "English" "source language". Should I use "destination language" or "target language" for "German"?
Both will be understood but target language sounds better and is probably the most commonly used expression to balance source language.
For instance, the wikipedia article about translation always uses the phrase "target language".
It seems that "target language" is used more frequently. The dictionary records target language as:
The language into which a text written in another language is to be translated.
However, it doesn't have any record of "destination language"
I think 'target language' would be better understood, and one would prefer to use 'target language', which is also the more correct term.