What is the difference between NAT and PAT (overload)?

That's PAT — port address translation, a.k.a. NAT overload — and it's what nearly every edge does. Static NAT is 1 private ↔ 1 public, permanent (for servers that must be reachable inbound). Dynamic NAT draws from a pool, still 1:1 while a flow is active. PAT multiplexes on ports: hundreds of inside hosts share one public IP because the router rewrites each flow's source to publicIP:uniquePort and keeps a translation table keyed by that port. 10.0.0.5:51000 → 203.0.113.1:62001, 10.0.0.9:51000 → 203.0.113.1:62002 — replies to those ports map back precisely. show ip nat translations shows the table live. The trade-off: inbound connections have no mapping until an inside host creates one, which is why unsolicited traffic dies at PAT without port-forwarding.