"Type I" and "Type II" errors are some of the stupidest and most obfuscatory academic terminology ever invented, and (as an academic) I absolutely refuse to make the effort to learn which way round they go. Just call the bloody things what they are: false positives and false negatives. (Getting seriously OT now, but Kahneman does something annoyingly similar with his talk of "System 1" and "System 2" in Thinking Fast and Slow).
As a computer scientist/programmer, there are three numbers, 0, 1, and infinity. If you're going to index your errors by the natural numbers, and you've got Type 1 Errors and Type 2 Errors, my next question is what a Type 3 Error is, and you know what my next question after that is.
Otherwise, please take this wisdom from programmers, who deal with this sort of thing all the time, and use an enumeration, in this case, {False Positive, False Negative} will do just fine.
When you are designing an hypothesis test the term positive and negative are not so clear. For example you can test that mean weight of bags is greater than 5.0 kg or smaller than 5.0 kg, both test are different, and some times you can accept both greater and smaller than 5.0 kg. The philosophy of hypotesis test is not as clear as a standard tests for pregnancy. In other terms,in some cases the H0 hypothesis is symmetric (>= versus =<) and is not clear what a positive result should be, you have to state clearly what is the H0 hypothesis. In a pregnancy test everyone agree than H0 is that you are not pregnant, that is in my HO the semantic difference between Type 1 error and false negative.
What are some synonyms to Kahneman's System 1 and System 2 then? Because Type 1 and 2 errors seem to be completely equivalent to false and positive negatives. I think Kahneman motivates his decision to introduce the terms System 1 and 2 quite well in his book, and I don't know of any direct counterparts.
Jonathan Haidt proposed a similar system in his book "The Happiness Hypothesis". He called it the automatic and controlled sides. The automatic side/system 1 is also what's being described in the book "The Inner Game of Tennis". I would summarize the two sides as the reflexive and the deliberate sides.
A false positive or false negative, can be like a pregnancy test.
A false positive, can be where the pregnancy test shows your wife is pregnant, but she is not. And the baby never arrives. Phew, dodged a bullet!
A false negative, can be where the pregnancy test shows your wife is not pregnant, but she really is. And 9 months later, a baby accidentally pops out. Oh crap!