It's to do with how they're made, which chemicals are used in the construction. One can't dictate on nature what pd will appear across the junction, just take what develops and use it to form batteries. For most purposes the tolerance between different types is not significant. If a gadget can't cope with rechargable batteries then IMO they were not well designed.
The maximum voltage obtainable from a CELL is 1.2v. A battery is the name given to a group of cells generally wired in series to obtain a higher voltage.