Actual determination of the DNA sequence in the shotgun approach?
The question appears to confuse the method of identifying and determining the order of bases in a fragment of DNA — Sanger* sequencing, Maxam–Gilbert or more modern ‘next generation’ methods — with the strategy for selecting fragments to analyse and reassemble into the larger contiguous sequence from which they were derived, of which shotgun sequencing is one.

Shotgun sequencing is a strategy in which the selection of fragments to sequence is random, the method of sequencing is a matter of choice (it was often the Sanger method when it was first developed), and the assembly is done by computer programs that identify matching stretches. (It fails — or is not completely successful — if by chance the fragments do not cover the whole DNA with suitable overlaps or there are certain types of repeated regions.)

Shotgun sequencing should be contrasted with what might be called ordered sequencing strategies in which one generally starts with a restriction map of the whole DNA and initially selects specific fragments to clone and sequence (by whatever method seems best). On the basis of the sequence of the fragment one can choose to sequence further from a position within the already sequenced fragment, and this procedure repeated. Here there is no apparent assembly step as this is inherent in the choice of fragments to sequence. (This is much slower than shotgun sequencing, and cannot be automated so that it is much more expensive. However, it is more precise.)

Coda

Part of the confusion may arise from the fact that modern automated methods of sequencing genomes are designed to work on a mixture of many uncloned fragments of DNA, so inherently involve the shotgun sequencing strategy. They tend to employ technologies other than the classic Sanger method. If a ‘manual’ clone-based ordered sequencing strategy is required to ‘finish’ missing or ambiguous regions of a genome, this would most employ the Sanger method of determining the sequence. Hence, the contemporary writer might employ what is, in fact, a misleading contrast.

*Fred Sanger was an eminent Nobel laureate, so his surname is capitalized.