Rabbi Aqiva Eiger (shu”t #136) says that there are two types of doubt, and each has its own mechanism for birur, for clarification.
The case of qavu’ah is one where the reality was once established. So in principle, there is a specific halakhah assigned already to this case. The doubt is in what that halakhah is. In this situation, we do not invoke rules like rov (majority), and every doubt is treated identically to an equal one.
The case of kol deparish is one where the reality was never established; this item never before stood out from the rest of the set. Therefore, we are assigning a halakhah to a case where the physical reality is in doubt. Here, majority is allowed.
Tosafos (Zivachim 72b, “Ela amar Rava”) write “qavuah only applies to a thing that is known”. Rabbi Aqiva Eiger explains that the piece of meat bought from the known store had an established halakhah. The buyer knew the state of the meat. We therefore call the halakhah “qavu’ah” — established. However, now it got mixed up, and we don’t know what that halakhah is. The doubt is in the halakhah.
However, if the meat is simply found, then the uncertainty begins one step earlier. We don’t know the state of the meat. The doubt is in the reality, what part of the set this item was parish — separated from.
I suggested a theory as to why this was true, based on first principles.
The Chinukh repeatedly explains various mitzvos by explaining “ha’adam nif’al lefi pe’ulaso — a person is affected according to his action.” Contemporary hashkafos differ over what halachic life is supposed to cause, whether the ideal is better described as “wholeness”, perfecting the image of G-d, or “attachment” to G-d…. But notice that both agree in describing the role of halakhah in terms of the change is causes on the self — whether perfecting him in a mussar sense, refining him in a Hirschian sense, bringing him experientially in a relationship with the A-lmighty, as Chassidim do, etc…
One thing this implies is that halakhah need not be concerned with determining an objective reality. Rather, it has to deal with that which has impact on the person — the world as it’s experienced. Perhaps this is why the realia to which we apply halakhah is called metzi’us, literally “what is found”, and substantive elements of the metzi’us are said to have mamashus, they can “be felt”.
Thus, if we do not know the reality, the metzi'us / mamashus is the resulting doubt. And thus, it makes sense that pesaq takes into account likelihood, as that is reflected in my doubt. But if we experienced reality, then halakhah was already established by that reality. And then it's not a matter of doubt, it's a matter of whether we are obligated to "play safe".
(I have what is likely a sefer's worth of material on the interplay of this phenomenology approach to metzi'us and halakhah at http://www.aishdas.org/asp/category/phenomenology . The above was snipped from there.)