To a Popperian, absolute certainty and partial certainy are very similar things. To Popper's opponents, they are also very similar things: some people who previously advocated certainty backed off to partial certainty, to try to dodge some criticism without changing their views substantially.
What the hell *is* partial certainty? It doesn't even make sense. One attempt to make sense out of it is to say it's a matter of probability. We can have a theory that is 90% likely to be true, or 99%, or whatever. No attempts of this sort have ever actually worked. You run into problems like how do you establish what the probability of some theory is?
The other main kind of partial certainty is you say some theory is well "supported". Or confirmed. Or verified. Or justified. If anyone tells you they aren't, you just say you didn't mean to provide any guarantees or certainty, they are just *pretty good* theories, pretty well established, pretty reliable. This is all crap. No one really has any coherent idea of what it means. All they do is take philosophy and a ways of thinking that were designed to work with Knowledge meaning Justified, True Belief, and don't change anything at all except saying it's not *absolutely* certainty it's just really quite compelling. So it goes like this. I point out what they are saying might be false. They say, "Whatever. I didn't claim it was perfect. It's pretty good though." So I say, "No, look, it could be false. All the evidence you have is consistent with it being false. How the hell do you know it's pretty good?" So then they say we have to act on the limited knowledge we have, which all points to their theory. And I say, no look, the limited knowledge we have is consistent with infinitely many theories, and you can't just pick out the one you liked in advance and insist we have to act on that one just because we don't have perfect information. Definitely by now, sometimes earlier, they stop speaking coherently, so that's that.
Why are absolute and partial certainty so similar? When one retreats from the stronger form he keeps in mind the same questions and problems. He's still on the same quest. What he wants is to justify and establish Knowledge. He yearns for certainty. He asks questions like how do we know, how can we prove, what would be strong support, which theory has more support, and so on.
Here's another way to put it: there are people who think they Know, and people who accept we are fallible. People after partial certainty are in the Know camp. All they are doing is wearing a disguise because they can't deal with the fallibilist criticisms of the Know position when the position is layed out clearly. So they just won't lay it out clearly anymore.
Aristotle claimed he Knew, and Socrates claimed he did not know. Before Aristotle, philosophers differentiated between Divine Knowledge (episteme) and human opinion (doxa). Human opinion means guesses or conjectural knowledge. It's fallible, useful, and capable of improvement. Divine knowledge is the perfect truth which only the Gods have access to. Aristotle didn't like that. He wanted full blown Knowledge for himself. He invented induction trying to get it. He came up with the idea that definition statements are infallible trying to get it. He destroyed the old distinction, which had been very wise, and claimed the authority to dictate justified, true beliefs. Since then, it went from divine knowledge to just knowledge, and everyone tries to get it, with science, with authority, with anylytic philosophy, with induction, with statistics, with scientism, and so on. And human opinion no longer has a single word of its own, and is ridiculed. No one wants it. They don't want guesses, they want to Know. And if they can't have any guarantees, they want to say they Almost Know. They have Partial Certainty. They'd give anything not to be fallible humans with mere conjectures.