The connection to the worldwide web is generally via hard wire between a modem and the network. That modem in turn is often connected directly to a router. From there it gets complicated.

As you know most routers (but not all) have both hard wire and RF (WiFi) connectivity to the devices on your local network (LAN). Just having this much gives you the ability to directly communicate with all the devices connected to the router. The path is from Device-A to the router to Device-B. However, it is also possible to communicate peer to peer, i.e. Device-A directly connected to Device-B. This peer to peer device connectivity is what Bluetooth is.
I've seen people with an earphone and microphone plugged into their heads. There is a wireless connection from that earpiece to their cell phone via Bluetooth. This peer to peer connectivity gives the user the ability to walk along the street apparently talking to themselves. They are actually talking into the microphone built into the earpiece which is stuck in their ear. That, in turn, is tethered via Bluetooth to the smartphone in their shirt pocket or purse or wherever. Another example of Bluetooth connections would be wireless speakers. Your computer can output music to the wireless speakers directly without going through the router, thanks to Bluetooth. The most familiar use of Bluetooth is with wireless mouses and keyboards. Of itself neither Bluetooth nor WiFi connects you to the Internet. You need something else to get you there; such as a modem. But to the uninitiated it looks like a direct connection to the Internet.
My printer, with the web server built into it, is connected to my router via WiFi. It's just another device on my LAN, but it's a device that can bypass my control of how it communicates to the outside world. I could simply connect it directly to my computer via hard wired Ethernet (or USB cable), but then nobody else on the network would be able to use it. Well, not easily.