Is the Internet nothing but a globally scattered interconnected routers, and that the connections between them could be via any of Leased Line, X.25, Frame Relay, ATM, MPLS, or Ethernet?
An internet (lower-case "i") is a network of networks. The Internet (upper-case "I") is the largest internet (network of networks). The networks comprising the Internet connect to each other by agreement of the network owners (companies) using BGP as the routing protocol. IP stands for Internet Protocol.
Layer 3 of the OSI model (IP) is the lowest layer that the Internet cares about. That means that any layer-1 or layer-2 protocols (PPP, ethernet, token-ring, FDDI, ARCNET, ATM, frame relay, HDLC, etc.) may be used on or between (or required, depending on the contractual arrangement between companies) any of the individual networks.
Each company (ISPs included) can directly connect to any other company with which it contracts, and the companies can change to which other companies they connect. In one sense, the Internet is simply a large collection of connection contracts.
... nothing but ...
No, definitely not.
Of course, the Internet is held together by routers, but those routers require a global numbering plan (like unambiguous public addresses), agreed-upon protocols (like DNS, SMTP, HTTP) and procedures to exchange information about each others' networks (like BGP), and some more "glue" (like centralized root DNS servers). All of those together make up the Internet.