Do cabled connections and Wi-Fi "use" the same bandwidth?
To borrow from U.S. Senator Ted Stevens, the Internet is a series of tubes. You have one tube coming into your house—the ISP connection plugged into your router.
Everything behind your router shares that tube—think of the Ethernet cables as a regular straw, and the Wi-Fi as a long, flexible straw. If someone on the Ethernet straw is drinking up all the bandwidth there's none left for the thirsty person on the Wi-Fi straw.
Additionally to what has already been said:
Downloading a large file does not directly influence bandwidth. As long as the file is being downloaded slowly, its size does not matter.
You also mentioned torrents. Torrents have a very interesting effect on networks.
downloading a torrent may significantly degrade your internet connection quality or that of other people sharing the same connection, including bandwidth and/or ping even without hogging the network's entire bandwidth.
By opening a large number of concurrent connections, a torrent can overload the processor of your router, which translates into a huge drop in overall networking performance (and even overheating in the worst case).uploading (seeding) a torrent can have the same effect as downloading one, but for a different reason.
A connection can only be established, when a client (you) makes a request to a server (upload a message). The server responds with some data (download), but since anything could happen to the data along the way, such as packet loss, the client needs to verify the data's integrity and report back to the server, either with an "I got the package, please send the rest", or with a "the package's corrupted, please send again".
If you're already using your entire upstream bandwidth for seeding, your or other computer on the same network may not have the necessary bandwidth for base communication.
Torrents do not have to be a networking dead-weight, as long as the torrent client is configured properly. Limit the maximum amount of connections to a reasonable value, and do not allow your client to use up the entire network's upstream.
There are plenty of good guides online for configuring a torrent client properly.
Yes, both methods consume the uplink bandwidth to your ISP. All traffic on your network that transits the router (downloads, video streaming, etc., etc.) shares the internet connection bandwidth.