we have a single sequence for each DNA molecule?

We would typically say "one continuous string of DNA sequence without gaps", i.e. 1 contig per chromosome.

It is easier to imagine this for bacteria with very small genomes, maybe this article (especially its supplement!) will help you to get a better understanding of this. I assume you've read Shannon Begley's account (or other's) about why complete sequencing of mammalian genomes hasn't happened yet

There was an effort to (re)define these standards at the start of next generation sequencing.

For higher Eukaryotic genomes we may not have "finished" genomes for a long while. Partly because current sequencing technologies are still not able to reliably sequence repeat/difficult regions (complete sequence of human X chromosome was just published, almost 2 decades after human genome was "done").

Like many software projects, a genome reaches v.1.0 status and then keeps evolving via major genome builds over time.