Data mining is the process of extracting useful information from data, such as patterns, trends, customer/user behavior, liking/disliking etc. This involves the use of algorithms that are related to Artificial Intelligence and statistics.
Wikipedia's definition of Data Mining is:
Data Mining (the analysis step of the Knowledge Discovery in Databases
process,[1] or KDD), a relatively young and interdisciplinary field of
computer science,[2][3] is the process of discovering new patterns
from large data sets involving methods from statistics and artificial
intelligence but also database management. In contrast to for example
machine learning, the emphasis lies on the discovery of previously
unknown patterns as opposed to generalizing known patterns to new
data.
Machine Learning involves making the computers "learn" that behavior, trend etc, and to act according. For example, in credit card fraud, the computer "learns" the behavior of a customer, and if something strange occurs (a transaction involving very high amounts etc), it flags that transaction for potential fraud.
Wikipedia's definition of machine learning is:
Machine learning, a branch of artificial intelligence, is a scientific
discipline concerned with the design and development of algorithms
that allow computers to evolve behaviors based on empirical data, such
as from sensor data or databases. Machine Learning is concerned with
the development of algorithms allowing the machine to learn via
inductive inference based on observing data that represents incomplete
information about statistical phenomenon. Classification which is also
referred to as pattern recognition, is an important task in Machine
Learning, by which machines “learn” to automatically recognize complex
patterns, to distinguish between exemplars based on their different
patterns, and to make intelligent decisions.
Machine learning uses Data Mining to learn the pattern, behavior, trend etc, because Data Mining is the way of extracting this information from a set of data. Data Mining and Machine Learning both use Statistics make decisions. So yes statistics is involved and is very important in Data Mining and Machine learning.