The Internet is made of cats according to the researchers on the YouTube rathergoodstuff channel, although a closer reading of their work reveals a more subtle cat - tube duality reflecting the popular perception of "Teh Internets" as both content and delivery channel.
Engineers make a clear distinction between the Internet (a global network of networks) and the Web (a distributed information space that uses the Internet to provide access to interlinked content through a combination of protocols, data formats and identifiers such as HTTP, HTML and URI).
"Browsing", "navigating" and "information discovery" are the kinds of generic activities that web developers and information scientists concern themselves with, but the more common labels Social Networking, Internet Video, Blogging, Online Banking, Open Source Development, Internet Porn, E-research and Internet Shopping describe what people are actually achieving with (and within) the (application-neutral) information space of "the Web".
These various categories of practice and activity are distinctive enough to have their own names and their own specialist kinds of interaction (shopping baskets, playlists, blogrolls) even though people may be simply (reductively) "navigating web pages" using the same technology (a Web browser connecting via HTTP to a Web server) on the same devices (a home desktop or laptop) to engage in all these activities.
Those web engineers and content providers building on the Web to provide Internet Shopping (e-commerce, b2b, secure financial transactions, product databases, stock control, warehouses and delivery) have different concerns to those dealing with Internet Video (rights acquisition, media streaming, content licensing, bandwidth negotiation, format transformation). The activity supporting each of these practices can be modelled as a network of stakeholders (providers, consumers, participants, brokers, technologies, marketing channels); looking in detail at any particular activity reveals a web of information and data. The Web as a whole is the conjunction of these individual activities - neither entirely separate, nor completely merged and integrated but overlapping and interacting, all built on the simple foundation of the Web architecture, but realised in different kinds of organisation drawn from different industries, with different expectations and rules, communicating through different kinds of sites, perhaps on different devices.
The bigger picture of the Web then is not a monolithic whole nor a homogenous distribution of uncoordinated components; it is rather a loose affiliation of semi-independent content networks (webs) with their own practices and technologies and business (sustainability) models, their own ecology of providers and consumers. Held together by W3C-mandated standards, policies and architectural overview, the Web at scale is a network of webs - the InterWebs - mutually reinforced and stabilised by each others success and contribution to the whole.