There is a bit of confusion, even from people who know a lot about technology, in the terms Wi-Fi and wireless. They are often used interchangeably, but they are really two different terms. In fact, in the past, I was guilty myself of misusing the terms.
First, wireless means, literally, without wires. That encompasses a lot, including your wireless keyboard and mouse, Bluetooth connections, but also your Internet connection. It’s really a general term and can, in certain situations, have nothing to do with the Internet. For example, when you plug in the USB receiver for your wireless keyboard, you don’t need an Internet connection to use the keyboard, it communicates wirelessly, through that receiver.
Wireless also has been used to refer to broadband Internet connections, such as you would use on your Smartphone or tablet. Wireless is a much more broad term than Wi-Fi.
Wi-Fi, refers to the standard you use to connect to the Internet. Wi-Fi is part of wireless, but is not the same thing. The term Wi-Fi indicates a specific communication standard to allow computers to share resources and files. You generally need a router or an access point to broadcast a Wi-Fi signal. To use Wi-Fi, the devices must be fairly close together because of the limited range of the signal.
One way to help understand that difference in wireless and Wi-Fi is to think of your Smart phone. When you’re using it in your home or business, you more than likely are connected to the Wi-Fi network. You’ll see the Wi-Fi icon to indicate you are connected. (By the way, I just discovered that the up and down arrows mean uploading and downloading, as a little bonus tip!)
However, if you get further away from any access points while using your phone, you will switch over to the wireless, or broadband/cellular network. This is usually indicated by the strength bars or a 3G/4G/LTE indicator.
So while you may have thought they were the same thing, wireless and Wi-Fi are really two different terms, but mean similar things. Just remember that Wi-Fi is specific to connecting to the Interent, whereas wireless is a more general term for using anything without wires.