Assume the 16 bit no. to be 256.
So,
byte 1 = Some binary no.
byte 2 = Some binary no.
But byte 1 also represents a 8 bit no.(Which could be an independent decimal number) and so does byte 2..
So how does the processor know that bytes 1,2 represent a single no. 256 and not two separate numbers
The processor would need to have another long type for that. I guess you could implement a software equivalent, but for the processor, these two bytes would still have individual values.
The processor could also have a special integer representation and machine instructions that handle these numbers. For example, most modern machines nowadays use twos-complement integers to represent negative numbers. In twos-complement, the most significant bit is used to differentiate negative numbers. So a twos-complement 8-bit integer can have a range of -128 (1000 0000) to 127 (0111 111).
You could easily have the most significant bit mean something else, so for example, when MSB is 0 we have integers from 0 (0000 0000) to 127 (0111 1111); when MSB is 1 we have integers from 256 (1000 0000) to 256 + 127 (1111 1111). Whether this is efficient or good architecture is another history.