Questions: Priming Sugar, Carbonation...

Hello!

I get a bit confused about priming sugar. Is there a difference in terms of making a dry, sparkling cider between

1) fermenting to dryness and adding sugar to bring up to 1.010 (as the Proulx-Nichols book suggests) and then bottling (in champagne bottles

or

2) bottling when the fermentation reaches 1.010 (also in champagne bottles) - which my cider has reached.

So - does the priming sugar somehow function differently? Explain the science to me, friends!

priming sugar is just sugar. nothing special about it. you can bottle now and get the same level of carbonation.