What do MAP@K and MRR show, and when is each appropriate?

MRR (mean reciprocal rank) looks only at the first relevant item: at position r the query contributes 1/r. It fits tasks with one right answer — autocomplete, continue-watching, a specific intent. MAP@K averages Precision over every position holding a relevant item, rewarding a densely relevant head. It fits feeds and carousels where the user scans several cards. Both are binary — relevant or not. With graded relevance, use NDCG instead.