I don't understand why some op-amps are specified as being dual rail, and others as single rail. Since (AFAIK) none have a ground pin, there is no difference between connecting the positive supply to +10v / the negative supply to -10v, or the positive supply to +20v and the negative supply to ground. Either way, the difference is 20v!
From a purely theoretical POV an opamp is nothing more than a (extremely large-gain) differential amplifier, i.e. an amplifier whose output is an amplified replica of the difference between its two inputs.
The problem with this view, usually found in introductory material/courses on opamps, is that it doesn't take into consideration how power is to be provided to the opamp. Input and output voltages are simply referred to ground, without showing how the component is supposed to know where the ground is (almost as if it were psychic)!
Of course you know that opamps have two power supply terminals, but neither one is labeled "ground", so how the opamp is supposed to know where ground level is? Well, it doesn't know! It simply assumes it is half-way between its two power supplies. That's why you power them up with a symmetric supply. If you didn't you wouldn't get 0V between output and ground when your inputs are shorted together (0 V differential input, and I'm neglecting common mode input to simplify things). The reason for this design choice is twofold:
opamps are meant to be used also as DC coupled amplifiers, therefore to amplify a differential signal, which can have either polarity, the output must be able to go negative, and for this to be possible you need a negative supply also.
For a single-supply DC coupled amplifier it is difficult to reach a 0V output level without special circuitry. Older opamps or opamps not meant to be "rail-to-rail" cannot force their output too near the rails, when the negative supply is grounded the output cannot reach 0V (usually the best you can have is 1V above ground, or there about).
Rail-to-rail opamps are designed with more sophisticated circuitry that can bring the output very near the rails (tens of millivolts, maybe less) so they can bring the output really near 0V when used with a single supply, especially if designed to be operated in single-supply mode.
As an aside, although theoretically it is possible to power an opamp with two different positive supplies (e.g. 5V and 25V), because the "difference is 20V", the problem is the other parts of the external circuit. If in such a setup you put a voltage of 0V across one input and ground, actually you are providing a -5V voltage relative to the "lower" 5V supply, which usually means frying something inside the opamp!
It is convenient in many applications to have a voltage reference point somewhere between the most positive rail and the most negative rail. This is usually called 0V.
0V can come from the power supply and feed to the op-amp circuit or, 0V can be "constructed" by using a potential divider and maybe another op-amp to produce a "mid-rail" signal. You can also generate a negative supply from a positive supply.
All op-amps that operate in linear circuits have to be "biased" somewhere in between the two power rails and this means either the input itself contains that bias naturally OR you have dual supplies OR you manufacture a mid-rail or negative rail. By "bias" I mean they have a dc operating point that is not end-stopped against the rails.
The upshot of what I'm trying to say is that op-amps don't care how you do this and if the data sheet specifies dual rail then a single rail of twice the voltage will be fine. I'm not saying this rule applies 100% because that would be stupid BUT I can't think of one so-called dual-rail op-amp that cannot work with a manufactured mid-rail.