If somebody says: We were writing songs as a four-piece.....

Does "writing" mean composing music or writing lyrics, or both? If writing means both composing music and writing lyrics how to differentiate what soemone is trying to say when he/she says: We were writing songs????

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Yes, "writing" can be used for both.

For just music, you can use "scoring" or "writing a score".
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Thank you for your explanations!
I'd disagree slightly, insofar that writing and composing are directly interchangable when referring to music or poetry, however I would read scoring more as a synonym of orchestration when applied to composition.