Yes, because your IP, the thing which identifies your computer (whichever OS it's running) is the same. The ISP (and, for that matter, any node along the data path, and a DNS server or two) must know the addresses of both the host and server in order for the Internet to work.
If you wish for anonymity when browsing, you'll have to run through a proxy server like www.anonymouse.com while online, which offers a modicum of protection. Then as far as the ISP is concerned, you're just looking at this proxy site the whole time (although it must be fairly obvious you're using it to obfuscate what you're actually looking at).
The best proxifier software is the TOR network, which is like a gigantic network of nodes that bounces your connection around all over the place and makes it next to impossible to tell who is looking at what. It does have its flaws, and unfortunately setting a computer up to use it is beyond the scope of this answer. Google it. Also be aware that websites can and do exist within the TOR network, but I caution against visiting those because by their anonymous, practically untraceable nature they can be host to some very, very, VERY illegal stuff. You can't really access them without specifically knowing what you're doing, though.
But yes, to answer your question, the IP is related to the machine connecting to the network (in a house this is usually the router, to which all the computers are attached via a LAN), so the actual software running on a particular computer matters not one bit.