When the people saw that Moshe delayed to come down from the mountain, the people gathered themselves together to Aharon, and said to him: "Rise, make us gods who shall go before us..." ... [Aharon] received [their golden rings], and fashioned it with a graving tool, and made it a molten calf; and they said: "These are your gods, O Israel, who brought you up out of the land of Egypt." When Aharon saw this, he built an altar before it; and Aaron proclaimed, saying: "Tomorrow is a festival to Hashem." (32:1-5)
The people ask Aharon to make "gods". Aharon makes a single calf (representing perhaps a single god). The people proclaim "These are our gods". Aharon responds by declaring a ceremony for Hashem, the one real God.
It is not clear who the people end up worshipping: one God, or a whole bunch of deities. But clearly Aharon has tried to direct their polytheistic enthusiasm into a monotheistic framework. If he succeeded in this, then the most severe aspect of the sin was avoided through his initiative.
Hashem smote the people, because they made the calf, which Aharon made. (32:35)
This line seems to be phrased awkwardly on purpose. Did the people make the calf... or Aharon... or both? The intent is to point out that Aharon made it - raising the possibility that he should be punished - and simultaneously to say that the people and not Aharon deserve to be punished by "smiting". Aharon was physically responsible for the calf, and he is certainly embarrassed when his brother comes down and sees him in charge of the whole scene, but here God decided not to punish him for it.
It is not fair to compare Aharon's actions to Moshe's at the time. The premise of the sin was that Moshe would not return and the people had to create new leadership for themselves. Once Moshe showed up, the calf worship immediately lost its basis. I suspect Aharon's course of action was the best possible under the circumstances. Better even than opposing the worship, getting martyred over it, and then having the people worship "gods" as they originally intended.