Two variations on sorting into categories. Multi-label means an item can belong to several at once, like a support ticket that is both a billing question and a complaint. Ordinal means the categories have an order, like satisfaction from very poor to very good, where being two categories out is worse than being one.
Technical view
Multi-label uses per-label sigmoid outputs with binary cross-entropy rather than a softmax, and evaluation by Hamming loss, subset accuracy, or per-label precision and recall with macro or micro averaging. Ordinal problems lose information under plain multi-class treatment; options include ordinal regression, cumulative link models, or thresholding a regression output. Label correlations matter in both and are commonly ignored.
Related
Part of AI Terminology Index, section: Classical Machine Learning.