Hi, Damian. The two stages are quite similar, but differ in their aims.
The contigging stage navigates the contig overlap graph to find paths between contigs linked by paired-end information, expands repeats and merges complete sequences without gaps. The contigging stage will only insert gaps where it believe there is a lack of sequencing data. It will not insert a gap to span a repeat that it cannot resolve. This algorithm is called SimpleGraph / MergePaths.
The scaffolding stage uses the contig overlap graph only incidentally and primarily uses the paired-end scaffold graph, which is the links between contigs inferred from paired-end reads. It does not expand repeats, and will insert gaps to scaffold over either sequencing gaps or repeats. This algorithm is called abyss-scaffold.