G'day mate, yes they do! In fact baluns do serve both purposes (depending). I don't wish to confuse all with theory but it's a fact.
Yes baluns do allow from a balanced to an unbalanced temination and vice versa and yes that is their main 'job' but they also provide impedance transformation eg. 1:1, 4:1, 9:1, 75 ohm to 300 ohm nominal, (an example of a 4:1 balun) etc etc.
The type of balun called the 'current' mode or 'choke' balun which I am very familiar with for transmitting applications can also function as an 'unun' (unbalanced to unbalanced), an excellent example of feedline 'decoupling', and also as a conventional 'balun'. So in actuality baluns can and do both things depending on the configuration. Regards, Felix (vk4fuq) aka catman.