These three kanji「労、 働、 努」are taught close together in grade 4. I've struggled a bit in separating them conceptually, and haven't found anything online in English that explains this distinction.
I've had a native speaker explain it to me in Japanese and I interpreted the distinction as the following:
働: It's your work, your job, i.e. what society pays you for, as in 働く
努: Applies to a level of effort in any manner of applying yourself, as in 努力 and 努める, which can be applied to outside of what one would consider a traditional job. Similar conceptually to 頑張る.
労: Also applies to your job, but more with regard to an outcome/effort level related to you applying yourself to it as in ご苦労様 and 労う.
Am I understanding this correctly?