Continuous - can mean a number of things. Spot month, probably, although this isn't universal - some use second month out.
This in itself makes no sense with "soft" commodities such as NG, which, amongst other things, is seasonal. Spot month can behave quite differently than further out months. Compare Oct, Nov and Dec NG contract charts, for example. They may as well be different commodities for anyone actually trading them.
You may find similar in many others which are not strictly financial, but even financials (FX, equities, bonds etc) have either contango or backwardation to deal with.
Then, is it adjusted, or spliced?
I personally never use continuous, and rarely spot month. They are a pox. Too many issues.
I'm always astonished when folk ask questions when their broker rolls their CFD into a new month. Children shouldn't play with matches. End Charting Basics 101 rant.