The internet connection
Your ISP provides an access connection using a technology such as fiber, cable, DSL, fixed wireless, cellular or satellite. That link has its own speed, latency, reliability and service-plan limits.
Wi‑Fi
Wi‑Fi is a wireless local-area networking technology based on the IEEE 802.11 family of standards. It connects nearby devices to a local network by radio. The network may have internet access, but Wi‑Fi can exist even when the internet service is down.
Ethernet
Ethernet is a wired local-network technology. A computer connected by Ethernet can use the same internet service as a phone connected by Wi‑Fi; only the local link is different.
Router
The router connects networks and usually acts as the gateway between your home LAN and the ISP. Consumer routers often combine routing, firewall, Ethernet switching and Wi‑Fi access-point functions in one box.
Why the distinction helps troubleshooting
If a wired device is fast but a Wi‑Fi device in one room is slow, the ISP may be fine and the local wireless link may be the bottleneck. If both wired and wireless devices are slow at the same time, the problem may be upstream, at the router, or with the service itself.