jouellet:
I thought that every element extracted from a string, would be considered as an ASCII character, therefore taking the full 8 bits ...
It's only an ASCII character if you decide it's an ASCII character. A byte (unsigned, so we don't have to worry about negative numbers), is simply a small unit of memory that will hold the numbers 0 through 255, or in another base, 0x00 through 0xff.
A string consisting of two ASCII numbers can definitely be held in a single byte, making it far better for storage in an EEPROM.
The Arduino is fast enough to do the conversion, both for making a string into a series of bytes for storage, and for making it into a string of bytes for comparison, without you sensing a slow operation