Is supervised machine learning by definition predictive?
A description as any statistic drawn from your sample data, say the sample mean, quantiles, etc.. Inference is a conclusion drawn from your sample data about the population, e.g., rejecting or accepting some hypothesis or stating that a model is suitable or not for describing your data. Prediction is simply a guess about future observations, which hopefully uses your data and some function/model of the data in a way to formulate that guess.

Both unsupervised and supervised learning methods aim to learn a function of the data that predicts another variable (typically called y) so both are drawing an inference (i.e., a model is well suited to describe your data, see the first sentence here). However, these two methods differ in what data is available. In supervised learning you are able to use an observed sample of y for training your model and in unsupervised learning, y is unobserved.

Hope that helps!