prior probability vs a priori probability What is the difference between "Prior probability" and "a priori probability"
Wikipedia have two distinct pages for them.
As of my inference i thought "Prior" and "a priori" are same, i.e., P(y) in Bayes' theorem
P(y,x) = P(x,y)P(y) / P(x)

Some people make a philosophical distinction, which is (somewhat
fuzzily) mentioned in the Wikipedia article on 'a priori'. 
I agree with you that, for better or worse, the two terms are used
almost interchangeably in Bayesian statistics. 
One difference in usage might be illustrated by the experiment
of rolling a die. You might decide 'a priori' that the dice
are fair, from which it follows that P(Even number) = 3/6 = 1/2.
This is not necessarily in a Bayesian framework. It is also
not very informative to say the decision is 'a prioi'. It would
be more helpful to say why you choose to believe the die is fair
(tradition, laziness, you've tested it a bit, you trust the
person who produced it, etc.).
It seems to me that the term 'prior' probability distribution is rarely, if ever,
seen outside of a Bayesian framework. 
The German philosopher Arthur Schopenhauer is quoted as saying,
"Philosophy is the systematic abuse of a terminology established
just for that purpose" (my translation). I think he would have
enjoyed your observation about the two Wikipedia pages.
Perhaps someone else will educate us both with a more compelling
distinction between the two terms that makes sense to both of us.
