Is there a good analogy that illustrates the difference between early DNA sequencing techniques and shotgun sequencing?
The public effort, led by Collins, relied on a physical map of each chromosome.  Very large pieces of genomic DNA were sub cloned into cloning vectors and used to create genomic libraries in cosmids, BACs and YACs.  The sub clones are ordered using hybridization probes from either known genes, or RFLP genetic markers. In this way a physical map of each chromosome was built up, and then the project would march down the ordered clones, sequencing the sub clones.  If the physical map is good then you have a very good idea of where the sequence comes from.

Shotgun sequencing, in contrast, involves randomly fragmenting the entire genome into small fragments (using sonication, for example), sub cloning those pieces and sequencing everything.

In the first method each base is sequenced a minimal number of times, whereas in the second approach each base ends up being sequenced many times (on average).

For a whole genome, shotgun sequencing requires an excellent computer algorithm to "assemble" the resulting data into overlapping contigs.