What does a battery's C rating mean and how does it relate to its maximum discharge current?
The way batteries are specified has a very long history. I don't like it either but I've learned to live with it.

An important thing you should know is that the capacity (C) is specified at a specific discharge rate and you need to know what that rate is. Sometimes it is specified like "C5" or C\$_5\$", which would mean that the rated capacity assumes that the discharge current is 1/5 of C.

If you discharge at a higher rate then the actual, available capacity will generally be less. Discharging at a lower rate generally provides a higher actual capacity.