Suppose I have a network with IP address 192.168.10.1/16.
You don't. The /16 part means that to get the network address you only consider the 192.168. and whatever address is behind is part of the host address.
192.168.10.1/16 means: the host IP address
192.168.10.1 which is part of the
So any address that begins with 192.168. and has a /16 prefix length is part of the same network, 192.168.0.0/16
192.168.10.1/17 means: the host IP address
192.168.10.1 which belong to the
Now we have two networks with the same numbers before the / and a different number after the /. What does that mean?
It means one of the network is the subnet of the other:
192.168.0.0/17 is a subnet of
If we cut
192.168.0.0/16 in two subnets we got
Note that you cannot use a network and subnet(s) of this network at the same time. Either you use the full network as is or you use its subnet(s).
In this specific case this is still easy to manipulate those numbers in decimal form, but to understand what's going on and manipulate any prefix length / network address, you really have to do it in binary form.
The answer linked in @Cown comment contains all the necessary information to perform those calculations.