How you set up your internal network is up to you. Your ISP provide the line and the router's public IP - and that's their point of demarcation.
If you set up your internal network in class A (10.x.y.z) you can have exponentially more hosts (16,777,216 or 2^24) because you sacrifice subnets for host bits. Class C network addressing limits you to 254 hosts per subnet, but gives a higher number of subnets with 254 hosts per subnet. Your ISP can't control how you set up your network internally, unless it specifically says so in your service agreement.