What joe says is correct regarding RFC1918 yes. However, the IPv4 internet addressing schema didn't start with ISPs since there weren't any 'end-users' in those days, but academic networks such as JANET in the UK which wanted to collaborate with one-another. They chose somewhat arbitrary IP blocks that they wanted before IANA was founded to control the allocations when usage increased and conflicts for IP space were more likely.
Obviously, the selection of IP addresses is irrelevant if there isn't a physical electrical connection between all the endpoints on the network. By which I mean multiple networks could use the same IP blocks without issue, until they wanted to talk to each other, and hence 'internet' is short for 'inter-connected networks', rather than intranet which refers to the inside of a single network.
There are other important aspects to consider too, such as routing and the difference between LAN and WAN.
As you probably know, IP addresses are used to route packets around a network and when they reach a router (aka layer 4 switch) they rely upon that router having a suitable entry in its routing table which relates to that IP address (or address block) to send it out on. Note: It is very important that the output route for a packet never be the same as the input route since this could lead to packets bouncing backwards and forwards, not getting any closer to their destination. The TTL (time-to-live) field was added to the IP header to avoid this specific issue (and permutations of it i.e. cyclic routes).
On any given network, IP addresses need to be unique, otherwise you can end up in the situation where a router's routing table contains two or more entries for the same address (and hence two or more output interfaces) leading to ambiguity and unpredictability of routing. Note: There are many practical workarounds to this kind of thing and indeed sometimes this is done deliberately for redundancy etc. but from a theoretical point of view (and when learning about networks to begin with) it is a bad thing.
LAN and WAN
This difference is actually already covered above, but not explicitly enough for it to be obvious. If you think of a LAN as network A, the WAN it's connected to (assuming typical home user scenario) as network B and the LAN the recipient is in to be network C, then all you have is a subset of the internet containing networks A, B and C.
The only difference from the internet's point of view is that networks A and C are likely to have a single WAN-side IP address which is routable over the internet. RFC1918 addresses such as 10.0.0.0/8 (and other address ranges not previously mentioned such as loopback, multicast and broadcast addresses) are specifically NOT
In fact if you break this down into what's really going on, you'll find that packets go from network A, to network A's ISP LAN, to a tier1 network carrier and then the ISP LAN for network C, and finally network C itself. Network B is just what a regular user perceives as 'the internet' and hence is a WAN from their perspective, but the actual WAN doesn't really exist until your packets leave your ISP onto the internet backbone - which is provided by tier 1 carriers such as Level 3.
I realise that's largely tangential to the OP question, but hopefully that gives you some useful context to understand what's going on in IP networks.