That's delayed-onset muscle soreness — DOMS — and it's completely normal, especially when you're new or you've upped your distance. The ache peaks a day or two after the effort, not immediately, because the soreness comes from your muscles repairing and adapting, not from "damage" in the alarming sense.
Gentle movement actually helps more than total rest — a walk or an easy day keeps blood flowing and tends to ease it faster than sitting still. It also fades as your body adapts; the runs that wreck you in month one barely register by month three.
Sharp, sudden, or one-sided pain is different from general all-over stiffness, and worth paying attention to. General soreness is just the sign you did something new.