This is a name for the type of drilling, not searching for diamonds. The drill bits use artifical diamonds on them due to their harness (hardess of 10 out of scale of Mohs scale of hardness 1-10).

There are different types of drill bits for different purposes. Some just to drill water bore holes, some for drilling rock chip samples (they get ejected out by pumping water through).

The coring discussed here is for the geologist to look at the underlying rock in a good state. So they can check quality etc. For example I use it in the coal mines on eploration sites. Like taking a plug out of a big cheese!