You have one byte, which is 8 bits
So far so good
which is 2^8
Your use of "which is" here seems to be the root of your confusion. A more precise statement is:
8 bits can represent 2^8 distinct values.
N bits can represent 2^N distinct values.
If this is unclear, it may help you to think about decimal digits (0-9). One decimal digit can represent 10 distinct values (0-9), two decimal digits can represent 10^2=100 distinct values (0-99), N decimal digits can represent 10^N distinct values.
A bit is literally a binary digit. One bit can represent two distinct values (0-1), two bits can represent four distinct values, and N bits can represent 2^N distinct values.
So eight bits can represent 2^8 distinct values, and sixteen bits can represent 2^16 distinct values.