Typical home internet
A typical home internet will involve some connection, usually over wires or fibreglass, maybe even radio / mobile / satellite, and maybe even some combination of these with fallback.
But ultimately it will end up on a box, a "router".
For most people that router will have WiFi. It will have a label or card or some such with the name of the WiFi and password, e.g. vodagin5A4C and password kjhasd87af, which you will have dutifully typed in to your iPhone and iPad, and so on, to make it all work.
For most people that WiFi connection is "the Internet".
If you change "Internet provider", the new provider sends a new box which you plug in and you have new WiFi details to use.
So for most people WiFi is "Internet"...
WiFi and Internet are separate things
In practice the WiFi and Internet connection are separate things. It is just that your provider has created a nice simple package that provides the whole solution. Which is nice.
The Internet connection is the wires/fibre/etc that connect to your router. The router will probably have an "Ethernet socket" on it, or several of them. The WiFi part is the radio link from that router to your devices. These are actually separate things.
You can also use switches, small devices that have multiple Ethernet ports, to make this simpler - e.g. one wire to your desk, and a switch allowing several things on your desk to connect using Ethernet cables. In some cases you can get a switch which provides power via the Ethernet cables - this can be useful for things like an Internet connected telephone, or cameras, etc. This also works for most TVs and set top boxes.
The "speed" you experience when accessing the Internet will basically be the lower of the speed of your Internet connection and the speed of your WiFi. If you have a large house or thick walls you may find the limiting factor is the WiFi. It can also be a bit unreliable. Using cables will be much more reliable and faster meaning the limiting factor is the Internet connection. So if using a computer at a desk, e.g. working from home, using wires is by far the better option. It does not stop you also using WiFi for things, at the same time.
This wiring is not specific to your Internet connection, if you change ISP, you simply connect the wiring you have installed to the new router they provide. The wiring is infrastructure in your home, just like electrical wiring or plumbing.
The next thing to realise is that you don't have to use the WiFi your ISP included in the router. You may be able to get a router without WiFI (perhaps even cheaper), or have it turned off. Some routers even have a button or switch to turn the WiFi off, or perhaps a setting you can change. You can leave it on, but better to turn off if not using it.
You may still want to use WiFi, obviously. WiFi uses an "access point" (AP). This is the radio part that you phone, etc, connects to. The router from your ISP has an AP built in to provide WiFi.
The clever bit is that you can have your own separate AP. You can even have more than one AP for the same WiFi network. If you have a large house you may want an AP each end of the house, or each floor. If you have thick walls (as I do) you may even want external (weatherproofed) APs to allow WiFi outside.
There is a lot of choice in terms of the WiFi APs you get. Ideally you use Ethernet cables to connect to these APs to your network (and to the router for your Internet connection). You can use a power over Ethernet switch with many APs meaning so that you only need an Ethernet cable and don't have to also run power to the APs. It is also possible to get APs that are designed to "mesh" - connecting from one AP to the next using radio - these need power but don't need the Ethernet cable. This is not as good as using cables to all APs, but sometimes is the best you can do.
At the end of the day it is all down to budget, there are APs that are hundreds of pounds, and there are cheaper ones. Ideally you want APs that are designed to work together so they "hand over" your connection as you move around the house making it seamless. You don't "see" lots of different "WiFi" - you see one WiFi that works everywhere in the house.
Much like running your own wiring and switches, these APs are yours to set up for the best working in your home. They are infrastructure in your home. If you change ISP you simply connect to the new ISPs router.
Of course, having sorted your (multiple) access points, you now see your nice strong WiFi signal strength. But remember, WiFi is not Internet!
If you have a "really good WiFi signal", that just means you are well connected to your AP. It does not have any bearing on speed or quality of your "Internet connection". A comment by @firstname.lastname@example.org: "This does seem to be a real cause of confusion. It took me a long time to explain to Mrs Wife why having a strong WiFi signal at both ends of a video call doesn't guarantee good call quality".
I name this WiFi ...
There are loads of more complex options, multiple networks with different firewalling and security, and so on, with different named WiFi (all on the same APs), and so on. But that is not necessary for most people.
So it is worth thinking about things separately. Sorting our your home network - quite separately from deciding on a suitable Internet access provider. Some people even change ISP to get "better WiFi", which, as you can see, is not necessary - pick an ISP because of the Internet connection, and make sure your home infrastructure does what you need.