Probably, almost everything is “on the internet”. The internet is a world-wide interconnected network. If it has an IP address (v4 or v6) it is on the internet.
What you will find is that most connections to the internet are connected via a firewall/router. What is behind that firewall may or may not be specifically accessible from the internet.
For example, except for internal web servers, a web server serving www info accessible by a browser - Chrome, Edge, IE, Safari) would be behind a firewall, but the firewall would be programmed - “if traffic comes in on port 80 or 443, route it to the server that provides web browser content.” There may or may not be a different server for FTP content, or there may be no FTP content. Similarly, the email server (if there is one locally) may be another server, but same firewall address; or the firewall may route the traffic first via a SPAM filter to remove dangerous and unappreciated email.
So the problem with the OP’s question is - anything that is designed to use an exterior IP address and accept any IP protocol - web, FTP, email, telnet, secure versions of those, DNS, VPN, etc. - is “on the internet.”
Behind those firewalls, which are on the internet, are massive amounts of additional data that are not normally accessible to the public. If you can (secure) telnet into a server from the internet, or get a Citrix windows session, and then on that server with your login session, access a database, or the company accounting system, or run Autocad and pull up a company blueprint - would you consider that data to be “on the internet”? All the files on your PC are not “on the internet” (we hope) but your PC is…
Even more confusing, some internet data is available only if you authenticate; it may be as simple as logging into your Amazon account; or it may involve doing a VPN and secondary validation first. That authentication may be limited to a very small group.
Perhaps what the OP is thinking of is private networks - in the days before the internet, when only really big companies could afford wide area connections - they would rent a “circuit” on a telecom provider. At first, these were actual private lines, but as telecom evolved, they became part of (sort of a timeshare connection) on the telecom’s digital network. The connection was not accessible in any way from the internet itself, unless one connected to a session behind the firewall at one of the ends or compromised the telecom system.
The private connections were (are) expensive but allow for more reliable higher volume connections, for businesses that really need that. For smaller businesses and for less expensive, lower volume connections, typically now there’s VPN’s - software at each end creates a “tunnel” where communications travel between ends over the internet with everything else, but are so well encrypted that they cannot be deciphered or spoofed.
Given the right credentials, there are probably very few systems (think NSA) that are not accessible some way from outside a company’s firewall with the appropriate mix of credentials.