WiFi and Broadband are very basic concepts. If you have to write a paper on them, I suggest reading the Wikipedia links top to bottom.
WiFi is the wireless network in my home, delivered by a WiFi access point, and recieved by my wireless enabled laptop.
Broadband is the generic term for the high speed internet access I have from Telecoms exchange to my house.
I access my broadband connection, using my WiFi link at home.
My WiFi connection has enough bandwidth to carry my broadband connection, so could probably also be called a broadband link.
Broadband could be Jetstream (a brand name for ADSL in New Zealand), cable (through Telstra), fiber optic cable, wireless (wifi and other RF methods, regular cellular (EVDO, UMTS, 1XRTT, GPRS, HSDPA etc) or an ethernet connection.
Wifi is a method of having your computer connected to a network (it might be the "Internet" or just a company/home network) without needing to have cables plugged in.
I am typing this message on my laptop, the only cable it has plugged into it is the power cable. When I load up the geekzone webpage it loads over the wireless connection.
Think of it the same way as you do your TV remote control.
Broadband is "High Speed" Internet. It is a way of having your computer connected to the Internet without needing to tie up your phone line and "dial up", it's an always-on connection.
You can have Broadband just fine without Wifi, but it means the computer you use must be plugged into the Broadband network via a cable. But if you wanted to be able to move around the house easily with your computer, you can then get wifi "added" to your network, plug the cable and the Internet will keep working.
If you have just the one PC (and it's not a laptop) then I see little point in getting Wifi. You probably just want Broadband, which will make using the Internet a lot more enjoyable as websites load up a lot faster.
WiFi.......is used within a house to connect 2 or more computers/devices together, its a 'networking standard'.....it is the connection WITHIN your house....it is not broadband so to speak...
Broadband is a term used to describe a fast internet connection, provided by an ISP (Telecom or Ihug for example).......it is the connection TO your house....and can be provided in many ways.....adsl, wireless, satelitte or cable (dont confuse wireless with WiFi)
Where you may be getting confused is with 'Wireless'.......
'Wireless' is not 'WiFi'.......wireless is the connection from an ISP...TO your house.......WIFI is a connection WITHIN your house.....both are wireless/require no wires.....but one is provided by the ISP...and the other is provided and managed by you.
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You can actually have fast network connections with narrowband and slow with broadband. In the correct sense of the term, the "broad" and "narrow" prefixes refer to the frequency band used to transmit the data. Means a high-frequency narrow electro-magnetic beam can carry more information than a low-frequency one, depending on signal modulation of course.