This is close to correct. Statistics (the old school kind) is just about computing summary metrics for large amounts of data. Probability is about deriving pr

This is close to correct. Statistics (the old school kind) is just about computing summary metrics for large amounts of data. Probability is about deriving properties of a sample from the population, based on population parameters. Statistical inference (what is usually meant by "statistics" these days) is about figuring out what sort of population parameters could have produced the sample at hand -- i.e. probability but backwards.