I say “hair-splitting,” but I think the philosophical difference between these fields is actually pretty profound.

• Statistics
• Proposes a set of possible models, and posits the existence of a “true” model within that set. This “true” model explains the observations.
• This description applies to frequentist and bayesian statistics.
• Both camps take their models seriously as descriptions of reality. They only differ in their description of epistemic state, and in their methods for generating that description.
• Attempts to quantify our epistemic state.
• Frequentists: confidence intervals, $$p$$-values
• Bayesians: posterior distributions; Bayes factors

• Machine Learning
• More pragmatic: what is useful?
• Seeks a model for accomplishing some task: e.g., prediction or decision making.
• Selects a model based on its performance at that task—fitness for purpose. (A splash of Darwinism.)
• Makes no pretense at determining truth—is fundamentally an engineering discipline.
• We may choose different models based on trade-offs between performance, available memory, available processing power, available data, or other details of the operating environment.
• Machine learning takes algorithmic concerns into account.
• Is there an efficient procedure for determining the best model?
• This is the result of its origins within computer science.

My personal inclinations can probably be guessed from these descriptions.

$$\blacksquare$$