I agree that Popper and Carnap's views are much more similar than they want to admit, especially if you look at some of the most influential Philosophers of Science in the later half of the 20th Century such as Kuhn and Feyerabend.
There are several key differences between Popper's and Carnap's Philosophy of Science. One of the crucial ones is about the problem of demarcation between metaphysics and Science. The early Carnap wanted to deem any thing that didnt pass the principle of Verification as meaningless, but rather Popper saw his theory of falisfication as being able to draw a line between metaphysics and Science and he noted that many successful scientific theorys were orginally metaphysical speculations. (Think of the Greek atomists)
They also envisaged a very different role for Philosophy. For example Popper was a metaphysical realist, but having such a debate was utterly absurd to Carnap as it was not empircally verified. Another example of where they had diverging opinons on the role of Philosophy is whether there are genuine Philosophical problems, Popper maintained there where while Carnap disagreed and thought one of the main roles of Philosophy was providing definitions in use. (A view he later abandoned, as he realised Scientists were much better equipped to perform this role)
Carnaps verification saw each new observation which verified a hypothesis as increasing the probability of the hypothesis as being true. Scientific hypothesis are held tentatively with each further observation increasing the likelihood of a hypothesis being true.
Popper's theory of falsification lead him to be an exponent of 'Corrobration' with empirically testing only providing a report on a theorys past success. As being an exponent of inductive scepticism, the premises of an inductive arguement give no reason for believeing its conclusion. This leaves Popper a real problem as its not clear how science should preceed with results of experiments providing only a report on its previous success. For Popper a theory becomes more corrobrated the more the theory has survived servere testing (Severe testing being tests which the theory has a low probability of passing). Though I believe Popper is still left with the pratical problem of induction.
Popper's exposition is designed to be more scientific than Carnap's.
Though to me it is not at all clear that Science actually works through a process of falisfication. With something like Hempel's hypothetico-deductive method along with taking social constraints into account providing a much better description of how science works.
Could I then make my conjecture that Popper and Carnap are really looking at the same thing from two different perspectives?
You could certainly make the conjecture that Popper's and Carnap's viewpoints are much closer than each of them would admit to. Espicially with the concentration placed on subjectivism and science in the late 20th century by the likes of Kuhn and Feyerabend.