Yes-No question in 2AFC staircase test I understand the task of a 2AFC test is to select one of the two stimuli presented (e.g. the stronger one), whereas in Yes-No test there is only one stimulus presented. But is it ok to ask a Yes-No question (e.g. was there a difference between A and B?) in a test with 2 stimuli? and can it still be called a 2AFC test? (Or is it valid to do Yes-No test with two stimuli?)

I am asking this with regard to a threshold test using a 2AFC transformed staircase  (2 down 1 up procedure). It'd be a lot easier for subject to respond whether there was a perceivable difference between two stimuli rather than having to choose the stronger one. As my main interest is to see just noticeable difference, which is stronger is not of a concern. However, I guess there must be a specific reason why one stimulus has to be chosen over the other in a 2AFC test (re bias and sensitivity?). And I wonder what would be the implication of using a Yes-No question instead.

Many thanks in advance for your answers.
Lets introduce some notation. Lets $S_i$, with $i = 1 ,2$, represents the different stimulus classes and $R_j$, with $j = 1, 2$, represents the different responses. In a one-interval task$^1$, $S_1$ is presented half the time and $S_2$ is presented half the time. In a typical two-interval task, stimulus $U_1 = &lt;S_1,S_2&gt;$ is presented half the time and and  $U_2 = &lt;S_2,S_1&gt;$ is presented the other half.

The responses $R_1$/$R_2$ can be yes/no, a/b, up/down, or anything you want and it does not matter in either the one or two interval cases. In the two interval case, it is just as valid to ask did the first interval contain the signal: YES -- NO? as which interval  contained the signal: 1 -- 2?

With a transformed staircase, you might run into problems. It is not clear exactly what you are proposing to do. If you always present $U_1$, or present $U_1$ half the time and $U_2$ the other half, then the response that causes you to increase the difference between $S_1$ and $S_2$ would always be $R_j$ (with whatever $j$ you arbitrarily choose based on your labeling of the responses). To get around this you could present some catch trials with $&lt;S_1, S_1&gt;$ and maybe even some $&lt;S_2, S_2&gt;$, but what happens if you get unlucky and get a bunch of $&lt;S_1, S_1&gt;$ trials in a row. You will likely keep reducing the difference between $S_1$ and $S_2$, but that is strange since the signal level is not relevant in the catch trials.

While you can probably get away with it, there are likely better procedures/methods (e.g., dual pair comparison)

$^1$ I study audition so am used to talking about temporal intervals while sometimes in vision multiple stimuli are presented across different regions of the visual field. From a signal detection vantage, it doesn't matter.