Petroleum engineers work on organic chemistry on a large scale. Examples might include those who design grease processes, refine fuels for various applications, and so on...
Power engineers work on large scale electric distribution projects from the generator facilities through the substations, and design heavy duty controls for large motors and the like.
Power engineering is a subset of Electrical Engineering, which can include RF design, computer hardware design, switching power supply design, and so on.
As for what they get paid, that depends upon where you are in the world, and what skills you bring to the job. An entry level salary is typically anywhere from US$30k to US$50k. A senior engineer can make US$100k - US$120k and up, depending on what they do.
But, again, that's where salaries are TODAY. In general, demand for engineers has been steady. But in this global economy, who knows what could happen. My career goes back over 25 years; and while I can't say I'm wealthy, I make a comfortable middle class living.
If you love this stuff, you probably won't starve. If you don't like it, well, you won't be happy.