Critical rationalism is the view propagated by Popper.
Popper does not give up truth.
His first point is, that we cannot prove general theorems in science, because we always have only finitely many observations. The next observation could refute the statement. Hence Popper gives up proving general theorems in science.
According to Popper our scientific theorems are hypotheses. One should create hypotheses which are testable. A test can confirm or refute a hypothesis. In the latter case, the hypothesis is false and we need a better hypothesis. But even a confirmed hypothesis is not proved. We do not know whether it is true.
Hence Popper replaces proof by falsifcation.
By eliminating false hypotheses we hope to approach truth, which is considered a limit term. Pointedly formulated by Gerhard Vollmer: "We err upwards."
Certainty is the personal feeling to have true knowledge. It is a subjectice term and does not guarantee truth.