As a non-biologist and non-chemist I always imagined the B and C viruses to be quite similar but apparently I'm quite wrong about this

They have a similar cell of infection the hepatocyte, however beyond that they are very different. Straight down to their genomes, hepatitis B has a genome comprised of Double stranded DNA, while Hep C has an RNA genome. Unfortunately I am not a virologist as such my knowledge of all of the specific differences between these two buggers is limited. But yeah, they are very different, its why we don't have a hepatitis C vaccine but do have one for hepatitis B. Thus there are not even similarities between the capsid proteins. I wish I knew more background info about these guys.