This might be the most pedantic thread (on my part, too) I was ever part of. :)
The earliest reference to VPN I can find in the RFCs, RFC2547, seems to call the "destination" (the network spanned by the tunnel) the VPN, not the tunnel itself:
"If all the sites in a VPN are owned by the same enterprise, the VPN
is a corporate "intranet". If the various sites in a VPN are owned
by different enterprises, the VPN is an "extranet". A site can be in
more than one VPN; e.g., in an intranet and several extranets. We
regard both intranets and extranets as VPNs."
A security-conscious VPN user might want to ensure that some or all
of the packets which traverse the backbone are authenticated and/or
encrypted.
I still think that VPNs were invented to connect smaller private networks to a larger private network together, where private != privacy. (But rather related to authorities, such as using "private IP addresses" in e.g. 10.0.0.0/8, instead of publicly routable ones.)
Privacy was a (good, likely popular) option, but just not part of the strict definition of what a VPN is (much unlike today).
Let's say you have an IPSec tunnel between a branch location and HQ site. The typical solution was GRE where you encapsulate it inside another IP packet that has public IPs only for the destination to decapsulate it. When VPNs came along they added privacy hence the name.
In networking you are not connecting two networks. You are interconnecting three networks! the branch would have its own subnet so would HQ but the VPN also would have its subnet all routed as separate networks. The tunnel network getting privacy because it traverses untrusted networks (back in the day it wasn't typically the interent but ATM, frame relay,T1,etc... "directly" between sites), that's where term cloud comes from FYI the untrusted magic ISP network in the sky.