I cannot locate this distinction in either edition of How We Think. To be sure, Dewey's analysis of reflective thinking does distinguish a process of searching ('hunting', p. 112 ) that culminates in a judgment. However, I cannot find a passage in which Dewey reserves the term 'critical' for the culminating act of judgment. In fact, the 1933 version of How We Think has fewer uses of 'critical' than the 1910 edition. The word 'critical' appears in the index to the earlier edition (under 'inference') but not in the later version's index.
In fact, in some places Dewey uses 'critical' and 'reflective' interchangeably. For instance, in a 1922 reply to Laurence Buermeyer, Dewey says that Buermeyer uses the word 'reasoning' 'to express what I call critical or reflective thinking -- thinking in its eulogistic sense'. (Dewey, 'An Analysis of Reflective Thought' The Journal of Philosophy 19 (1922): 29-38, at 31, n. 2, emphasis added)
Perhaps Dewey made the distinction in question in one of his other works (which are many).
The distinction is in accordance with the etymology of 'critic' and its cognates. The English word has its source in the ancient Greek verb krino, which implies sifting or selecting, or forming a discriminating judgment. (Dewey uses 'sifting' on p. 101 and p. 102. ) The related Greek phrase kritikós indicates an ability to discern and decide. So, there is the notion of weighing or assessing something (e.g., evidence) in view of some at least tacit standards; there is also the implication of acting, or making a decision. The act is typically one of judgment. Roughly, then, one who has good judgment, or a keen critical sense, is able to decide how to judge based on some discerning insight. (Note that in German, 'beurteilen' is used to clarify kritikós.)
It is safe to say that Dewey was familiar with this etymology. According to Jay Martin's biography, Dewey studied ancient Greek in high school for three years. Moreover, the process that Dewey outlines conforms to standard interpretations of kritikós; for Dewey repeatedly emphasizes that reflective (or critical) thinking involves a searching and sifting (or 'hunting') stage, which is followed by a decision to issue a judgment. For example, in the first chapter of How We Think, Dewey writes, 'Reflective thinking, in short, means judgment suspended during further inquiry; and suspense is likely to be somewhat painful.' (1910, p. 13) Later, he says, 'The essence of critical thinking is suspended judgment; and the essence of this suspense is inquiry to determine the nature of the problem before proceeding to attempts at its solution'. (1910, p. 74) Both versions of How We Think contain this sentence: 'The judgment when formed is a decision; it closes, or concludes, the question at issue.' (1910, p. 107; 1933, p. 126)
Here, the decision that terminates the search process is usually a choice, or a free action; for it is often within our power (says Dewey) to suspend or postpone it. In addition, Dewey takes the overall process of reflective (or critical) thinking to be essential to our autonomy. In both versions of How We Think, Dewey writes:
Genuine freedom, in short, is intellectual; it rests in the trained power of thought, in ability to 'turn things over,' to look at matters deliberately, to judge whether the amount and kind of evidence requisite for decision is at hand, and if not, to tell where and how to seek such evidence. (1910, pp. 66-7; 1933, p. 90)