I think thats up to debate.

Wikipedia says:

A virtual private network (VPN) is an overlay network that uses network virtualization to extend a private network across a public network, such as the Internet, via the use of encryption and tunneling protocols. In a VPN, a tunneling protocol is used to transfer network messages from one network host to another. Host-to-network VPNs are commonly used by organisations to allow off-site users secure access to an office network over the Internet. Site-to-site VPNs connect two networks, such as an office network and a datacenter.

So my argument is, if it is not used for private communication between multiple clients, it's not really a VPN.

Lets say, we both connect to the same Proton VPN server - our computers would not see each other and would not be able to connect to each other via that service. It has effectively the same function as a proxy - making your public internet traffic appear to come from the IP of the proxy server instead of your home IP.

Whereas if you set one up yourself with openVPN for example, we could make it so that we both get a VPN internal IP that we could use to directly connect and idk, play minecraft or something. Instead of connecting through the public internet, we would connect through a virtual network that is private for the two of us.