Yes

It's preposterous to check 100 dictionaries to find out how a professional logician is using a technical term in a technical context. You did indeed ask if your perception was right or wrong and I explained why it was wrong, this by explaining exactly how I was using the term.

As it turned out, Merriam Webster, American Heritage, and Encarta are right but in part misleading, since the term "countable" is itself a technical term that should be disregarded in this context (or used as I defined it).

You say that "none of those definitions or synonyms hint that 'denumerable' and 'infinite' are kin if not quite the same". Surely any set of things whose members can be put in a one-to-one correspondence with the positive integers has to be infinite, since there are (obviously?) infinitely many positive integers. But the converse is not necessarily so: it's not the case that every infinite set is the same size as the set of positive integers. The infinitely many sets of positive integers can't be put in a one-to-one corespondence with the positive integers themselves...there are too many of the former. Ditto for the infinite set of points on a one-inch line. That's why I didn't use the word "infinite"...because it is the wrong word for the purpose. The right word is "denumerable". I could have used the synonymous "countably infinite", but I don't think that would clarify anything.