Coverage and depth are not identical concepts, though are related.

samtools depth will give you the depth at each coordinate,

samtools coverage can directly report other characteristics as well: for example what percent of bases are covered

http://www.htslib.org/doc/samtools-coverage.html

samtools coverage can be thought of as a convenience utility added later, well after samtools depth. You can compute everything that samtools coverage reports from samtools depth output with a custom data analysis process.