A stateless service keeps request state outside the instance (e.g., in a DB/Redis), so any instance can handle any request. A stateful service keeps state in memory on a specific instance, which makes scaling and failover harder (you need sticky sessions or state replication).
Expanding on the short answer — what usually matters in practice:
A tiny example (an explanation template):
// Example: discuss trade-offs for "stateless-vs-stateful-service:-what-is-the-diffe"
function explain() {
// Start from the core idea:
// A stateless service keeps request state outside the instance (e.g., in a DB/Redis), so any
}