There's really no difference.
Quoting from here,
What if I change the person's name?
To state a defamation claim, the person claiming defamation need not be mentioned by name—the plaintiff only needs to be reasonably identifiable. So if you defame the "government executive who makes his home at 1600 Pennsylvania Avenue," it is still reasonably identifiable as the president.
What does the whole thing depend on? It depends on how easy it is to identify the pseudonym-using plaintiff. They don't have more recourse, per se - nor do they have more protection under the law - but it may be harder for them to win the case. On the upside, the statement might not cause them as much harm when compared to a person using their actual name.