The two statements are very different, and it isn't even related to the "absolute" part of it. The latter, 2, clearly presents a positive and unsubstantiated axiom. It is also speaking broadly about external and real and infinite set of things and presenting a categorical claim. While it might be possible to conceive of a world in which that statement is true, we have no justification that it is true, and it would seem that it was chosen arbitrarily. Therefore, it would be uncompelling to accept it as true, and it certainly isn't something that can be affirmed from typical models for knowledge.
The former, 1, presents a very limited factual claim about the speaker's mental state, merely stating that he does not know. At the time, there were not such rigorous models describing what it means to "know", but intuitively we see knowledge as somehow being a reliable tool which is in some way related to a reliable method of justification. The speaker can consider several things which he might suspect he knows only to discover that he could not reliably know them, and this investigation could itself be seen as justification of a sort that is more reliable than for his other attempts at knowledge. Thus, his degree of confidence in the first know is greater to some significant amount than in the second set of "know"s. Since it is speaking merely about his mental state, rather than an external state, the speaker can be seen as a sufficiently reliable source of information and it is from a sufficiently limited scope that he might be capable of making such a claim.
I also want to point out that they are different in that 1 is talking about knowledge and 2 is talking about truths. Truth is, in popular models, a component of knowledge, but the inverse is not true. In other words, even if we cannot possibly know a thing, that doesn't affect whether or not that thing is true. Therefore, knowledge is a much more achievable bar to affirm than truth.
1 is also a starting point where 2 is a stopping point. 1 invites us to attempt to try to find things which we can know, while 2 provides a hard stop in finding any truth (and therefore, probably knowledge).
We simply cannot know that there are not absolute truths, and if there are, we cannot know that we could not somehow know them, or at least some of them. Positive claims need to be supported. We can be aware, however, that we lack any method to naively arrive at consistent conclusions. In other words, if we do have some capacity to know absolute truth, it isn't obvious. This is different than stating that we cannot know anything, and it certainly isn't making a claim that there is nothing true.