Naphtha is a VERY general term referring to the rough boiling range of a mixture of hydrocarbons.
Naphthas go form 50F initial boiling point up to about 450F final boiling point.
Lighter fluid is a light naphtha, but the front end is cut off to give it a higher flashpoint, does not evaporate quickly out of the lighter, and is low odor. It's mostly paraffinic so it burns clean in a flame. It could be straight run (straight distilled from crude), or hydrocracked.
Yes gasoline contains naphths, but the naphtha used for lighters would be very low octane.
Diesel fuel, or the component gasoil would be way too high flash to light in a lighter. Throw a match in a bucket of diesel fuel, and it'll put out the match.