Not actually right in my opinion. They all mean working, however, 工作 feels neutral. 打工, as far as I know, means some kind of work that is not stable, or not well paid, or something involves a lot of hardship, or all of them. So, it contains some feeling of scorn maybe. And when people deride themselves, they would refer themselves as 打工仔

If YouTube channel is acceptable to you, I would suggest "Wen Zhao Official文昭谈古论今". It seems to be the most subscribed Chinese self media on YouTube. It focuses mainly on politics which is a good way to learn about current China. And it also has content in text form, however, paied subscription is needed. Besides, the youtuber speaks decent Mandarin Chinese withou accent.