It's naturally very tempting to assimilate Aquinas's First Way and Second Way to each other. They both are arguments to the existence of God as first cause uncaused, both are based on originating causes (in the first way, moving cause or cause of change, following Aristotle; in the second way, making cause or cause of existence, following Avicenna), both proceed by eliminating the possibility of an infinite regress. And one could indeed assimilate them -- that is, we can easily run an efficient-cause argument that is structurally like the First Way, and we can easily run a moving-cause argument that is structurally like the Second Way. But the First Way and the Second Way as Aquinas presents them have important structural differences.
When Aquinas introduces the First Way, he says it is taken from change (sumitur ex parte motus). This is what we find. It begins not with the cause but with the result of the cause, in this case, being changed, as something we find in the world. It then concludes all being-changed requires a distinct changer on the basis of the Aristotelian account of change as the act of the potential insofar as it is potential. Since moving causes can nest, the only question is whether the resulting series stops (first mover) or doesn't (infinite regress). Infinite regress is eliminated because change requires a changer, that is the outcome requires a cause, and due to the nesting character of moving causes, an infinite regress gives you an outcome without a cause.
When Aquinas introduces the Second Way, however, he says it is from the notion or nature of the efficient cause (ex ratione causae efficientis). Thus before we even are given the argument, we have a difference between the First Way and the Second Way: the First Way is from the nature of the result; the Second Way is from the nature of the cause. And this latter is exactly what we find in the second way. The Second Way does not, as one might have expected, begin with effects. It begins with the order of efficient causes (ordinem causarum efficientem). We do not find an order of efficient causes in which an efficient cause is in any way ordered to cause itself to exist, because this is not possible based on the account of efficient cause as prior in being. Thus 'nothing is efficient cause of itself' is derived (exactly as Aquinas said) from the notion of efficient cause, which contrasts with 'whatever is changed is changed by another', which was derived from the notion of being changed. The argument for eliminating infinite regress has often puzzled philosophers recently, because it can easily be read as saying that we cannot have an infinite regress because there must be a first, which is opaque at best and easily interpreted as question-begging. But this is because it's read as if it were an argument from the effects. In fact, the argument for eliminating infinite regress is based, again, on the order of efficient causes, and very explicitly (in omnibus causis efficientibus ordinatis). Aquinas's argument is that, given that it is intrinsic to the notion of an efficient cause to be prior, an order of efficient causes has to have the structure of first-middle-last, however complicated the middle might be. (And notice again that the ultimate term here is not the effect but the last cause in the series.) Therefore, given that efficient causes nest in an order, an infinite regress of efficient causes would be an order of efficient causes in which the foundation of efficient-cause ordering, priority, breaks down, since the infinite middle-last series cannot be efficient cause of itself and yet would have nothing prior that could be efficient cause. The middle and last in an order are defined relative to a first, which is removed in the infinite regress.
The Second Way, in fact, doesn't talk about effects directly at all, except insofar as one efficient cause can be the effect of another in an order of efficient causes. It's all about the causes. Whereas the First Way gets the unmoved first moving cause from infinite regress causing a contradiction in the outcome, the Second Way gets the uncaused first efficient cause from infinite regress causing a contradiction in the order of causes.
This, incidentally, perhaps explains a peculiarity of the Third Way, as well, namely, that it explicitly refers to the Second Way, the only one of the Five Ways that relies on another of the Five Ways. But the Third Way is, like the second way, an argument in which we find efficient causes; efficient causes are causes of being and the Third Way depends explicitly on the principle that things possible-to-be-and-not-be begin to be from things that have being, which is an efficient-cause principle. Nonetheless, the Third Way does not mention efficient causes explicitly until it refers to the Second Way. This is because the emphasis in the Third Way is on the effects -- we start with effects that are possible-to-be-and-not-be, and get to something that is necessary; if it is not an effect, we are at a being having its own necessity and not receiving it from another, but if it is an effect, the same argument that was used in the Second Way gets us to such a being. Thus the Second Way and Third Way have a lot in common; but the Second Way is based on the nature of causes and the Third Way is based on the nature of effects.
