There isn't a difference. The terminology in England and Wales that means the same thing is "litigant in person", with the source of these Latin phrases have abandoned them in favor of plain English terminology.
The variation of usage, however, does not necessarily break down on a federal v. state court basis. Pro se is the majority usage, but the variation is more regional, within state courts, than it is a federal v. state divide. California and Michigan, for example, use both terms and use them interchangeably. If there is a historical reason for the variation in terminology, I haven't groked it.
Incidentally, there was historically a subtle distinction between the two concepts related to consent to the personal jurisdiction of the court that has long since become obsolete (more than a century ago), but which movements such as the "sovereign person" movement errantly believe has great legal importance to the power of a court over them.