How does a computer determine the data type of a byte?
Your suspicion is correct. The CPU doesn't care about the semantics of your data. Sometimes, though, it does make a difference. For example, some arithmetic operations produce different results when the arguments are semantically signed or unsigned. In that case you need to tell the CPU which interpretation you intended. 

It is up to the programmer to make sense of her data. The CPU only obeys orders, blissfully unaware of their meaning or goals.