Are you being sarcastic? The difference is visibility. It doesn't get much more clear and concise than that.
There are undoubtedly a number of expats who don't know exactly what a "persona fisica" is in the first place.
Without knowing what it means (and that many of them actually are "personas fisicas"), it doesn't help very much to to know that "pesonas jurdicias" are "invisible persons" or corporations. In fact, it probably adds to their confusion.
A persona fiscia is, according to AFIP:
El mismo permitirá, a las personas físicas, sucesiones indivisas o responsables por deuda ajena, cumplir con su obligación de presentación de declaración jurada de cada uno de los impuestos. Dichas declaraciones juradas contendrán: datos identificatorios, materia imponible, determinación del impuesto y saldo a ingresar. Estas declaraciones juradas deberán ser presentadas hasta la fecha de vencimiento, según el tipo de contribuyente, por transferencia electrónica de datos mediante clave fiscal reglamentada por la RG 1345 sus modificatorias y complementarias. Versión 15.0 aprobada por la Resolución General N° 3610/2014.
If someone uses an on line translator like freetranslation.com they will get the following:
The same will, to natural persons, or formed sequences responsible for the debt of the other, to fulfill his obligation of filing of affidavit of each of the taxes. These affidavits contain: identifying data, taxable, determination of the tax and balance to enter. These affidavits should be submitted to the maturity date, depending on the type of taxpayer, by electronic transfer of data through key fiscal regulated by the RG 1345 its transformative and complementary. Version 15.0 adopted by the General Resolution N° 3610/2014.
In other words, if I understand correctly, a "persona fiscia" is an individual who is responsible to declare income and pay taxes on time and a "persona jurdicia" is a corporation which has the same obligation.