To be sure. Where the rules say you are aligned or devoted to a path of chaos, does that mean the same thing as embracing a path, or are these specific and unique terms?

Thanks

You can be aligned to a god and don't even know it (in renegate description there is something that they often don't even know that they are serving chaos and gifts of the gods are big suprise for them). Often alignment means that a specific god has found some interest in you rather that you are actively praising him. Depends on character really.

Yes i understand that, but in pure mechanical terms are these words interchangeable?

In other words does having 5 more advances of the same god mean that you get access to the Rewards of the Chaos Gods (not just the Gifts), as well as the Marks, and the means to earn corruption/infamy confered by 'embracing' a given god.

Mechanically yes (after you check your alignment which happens every time you pass next 10 cp). if you want to stay unaligned, you have to watch your advances.