To get a count you would have to map the network topology of who has channels with who. I would guess there are greater than one network because not everyone is connected to everyone on lightning. Not all nodes are routing to every other node. It would be an interesting research project to see if there are distinctly separate networks of nodes sharing routes and how many separate networks there are.

There is no one LN, there are as many LN as channels built among LN nodes.

Technically both of these are true