We're not all connected to the same network. We are connected to different networks only the protocols operating on top of these networks allow the different networks to communicate with each other.

It was that way back in the 80s - there were other networks. BITNET connected some universities but not all of them. ARPANET connected some government contractors and researchers but not all of them. There were others but my memory gets fuzzy after that.

The Internet is an internet (note the capitalization difference) connecting some of these older networks and became the surviving entity of all of them.