Ian White wrote,

"Sorry, but it all seems to come down to the definitions of "current
balun" and "transmission line transformer" that one chooses to adopt.
Rather than referencing those definitions, please can you quote them
here, in full?"

I agree. In fact, in thinking about it, I realized that I'm more
likely to use the terms "choke balun" and "transformer balun" than
current and voltage balun.

Roy's analysis of (1:1 current/choke) baluns, available at
http://eznec.com/misc/ibalun.txt, may be interesting reading for
lurkers here who may be confused by this thread.

Cheers,
Tom