Data mining is a process of discovering patterns in large data sets involving methods at the intersection of machine learning, statistics, and database systems.
As you said, data mining is a process of knowledge data discovery (KDD) in a dataset that involves machine learning and statistical methods.
Besides those important phases from the Fayyad (1996) figure, the results phase's evaluation and interpretability are very important.
We can't neglect this phase; once the main concern was running machine learning algorithms and fitting them to get the best metrics.
Good metrics and results are very awesome, no doubt. However, we are concerned about how we can effectively contribute through the process, techniques, and methodologies to solve the real world's problems.
I know that many researchers have this concern already, but worth remembering that for the new researchers' ones.