Cara:

It might be interesting to consider how the various suffixes are chosen for these eponymous words.

For instance:

Why does a follower of Karl Marx become a "Marxist" ...

while a follower of Christ becomes a "Christian" ...

while something dating back to the presidency of Thomas Jefferson is "Jeffersonian" and to the era of Queen Victoria "Victorian" ...

while someone from Windsor is a "Windsorite" while someone from Phildadelphia is a "Philadelphian"?

In summ:

Why couldn't a "Marxist" be a "Marxian"?

A "Marxist" is certainly a "Marxian", but is a "Marxian" necessarily a "Marxist"?

"Soon after the death of Karl Marx, a Marxian school of economics emerged under the leadership of Marx's inner circle of companions and co-writers, notably Friedrich Engels and Karl Kautsky, both of whom were German."

http://cepa.newschool.edu/het/schools/marxian.htm

Marxian
[Dictionary.com]
"One who studies, advocates, or makes use of Karl Marx's philosophical or socioeconomic concepts as a method of analysis and interpretation, as in political economy or historical or literary criticism."

From this definition, it would seem that one could be a Marxian studying Marx's socioeconomic concepts without actually being a "Marxist".

Which brings us back to where we started:

How is an "ist" suffix different than an "ian" suffix, assuming there is any difference at all?

And, if there is no deliberate and systematic difference in meaning, on what basis is the "ist" ending chosen over the "ian" ending, and vice versa?