I don't get your question. What do you mean: "the network"? Are you referring to the internet?
How does it matter? If you're not connected to the "network" --- and I assume your referring to the your Internet connection --- then, you're not going to be "connected". You can't access the Internet.
To go further --- you asked "why does it matter HOW your computer is connected". To answer that, I assume you're asking about your "platform", as in Windows, Mac, Unix, etc. In that case, it doesn't matter.
All platforms are capable of accessing the 'net.
If you're asking about the methodology of "connecting", such as "dial-up" modems versus DSL or high-speed cable access, then there is a difference.
Not sure about what you're asking. Re-phrase your question so that we can help you.
A node is a device connected to a network such as a computer or a game console. (Each device connected to a network is referred to as a node. A node can be a computer, printer, game console, or router.)
Server.
Personal Computer is the computer that is not connected unto any other computer. Network Computer are computers that are inter-connected with each others. Network Computer can access any other computers files/data from one another.
This is usually used to describe the Internet. A few computers connected together is a computer network. A few computer networks connected together is a network of networks.
A node
Any computer which is connected to network and has unique ip address for the network.
It is known as a local printer, as opposed to a network printer, which is a printer connected to a network.
A resource network.When for data sharing computer is connected to a network it is a Resource Network.
Two or more computers connected together create a computer network. Computers within a network can interchange data.
A personal computer that is connected to a network is called a workstation or terminal.
A workstation
LAN