Practical Subnetting

I need to better understand subnetting. I understand it according to class. ie, Class A – 255.0.0.0, Class B – 255.255.0 etc.

However, a Class C is 255.255.255.0. Hypothetically this allows 256 hosts. If a server is 192.168.0.1 with a subnet mask of 255.255.255.240,

Could a client to that server have…
*IP 192.168.0.1 with a different subnet?
*Or a different IP with the same subnet?
*Or a different IP and a different subnet.

I need a practical description. Please help.