Kant's primary emphasis in his ethical writings - certainly the Groundwork and the Critique of Practical Reason - is on our rational nature. Just as theoretical reason works on unconditional, universalisable rules (such as modus ponens in logic), so practical reason should display an analogue. It too should operate under unconditional, universalisable rules. Two examples of these are the two formulations you quote of the CI.
Practical reason in the sense that is central to Kant's ethical theory is not instrumental, means/ end rationality - the calculation of efficient means to clearly conceived ends. Kantian practical reason is about consistency. 'Act only in accordance with that maxim which you can at the same time will that it become a universal law' (Groundwork, 421 : M. Gregor tr.). One way of putting it is to say that the CI embodies rationality in the sense of mutual consistency : we can all act on the CI without mutual self-defeatingness or conflict. (Just as we can all use modus ponens in theoretical reason without its causing conflicting views.)
Kant's view is that there is a co-incidence between the consistent conduct (personal and interpersonal) that the CI requires and the conduct required by morality - at least by ordinary moral thinking. This is a major part of the point of his four moral examples in the Groundwork. What the CI rules out or requires, so too does ordinary moral thinking as embodied in the four examples.
He does not, so far as I can see, explain the nature of this co-incidence. He presumably doesn't see it as purely chance, a mere contingency, but he also doesn't show how the requirements of the CI and of ordinary moral thinking necessarily co-incide. He assumes that they do.
There are reasons to doubt that they actually do so. It is not at all clear that if the CI does rule out suicide (G 421-2), for example, ordinary moral thinking agrees in condemning suicide in Kant's unconditional terms.
There is a further point. In Kant's view the summum bonum, supreme good, for humanity is the combination of virtue and happiness. But there is no rational connection, certainly no entailment, between acting on the CI and achieving happiness in the present life. Indeed, happiness may be defeated through the fact that the CI can and often does require us to act contrary to self-interest. Since it is rational to desire at our supreme good, the summum bonum, acting morally can be irrrational because it requires us to act against our own happiness insofar as it bids us act contrary to self-interest. Kant recognises that the pursuit of self-interest has a kind of rationality even though it falls low in the scales vis-a-vis the consistency embodied in the CI. Also happiness includes self-interest (which is not the same as selfishness) and is recognised as a part of the summum bonum.
Kant's response to this problem, namely that acting morally, acting on the CI, does not guarantee happiness, so that the summum bonum is not necessarily within our grasp in the present life - indeed, seldom is so - by arguing for the rationality of faith in God, the afterlife and the immortal soul. In the afterlife, happiness and morality coalesce. God puts together what an imperfect world has separated.
The trouble is that in the Critical Philosophy the existence of God, the afterlife and the immortal soul are all unprovable. What Kant calls rational faith, some others would regard as wishful thinking. There are Kantian atheists and Kant cannot demonstrate that his post-mortem reconciliation of happiness and morality is anything more than a desideratum (a 'nice if') rather than a fact.
Hope this helps. I'll try to clarify if anything looks obscure or false to what Kant says.