Let's label them inertial conservatism and objective conservatism. Where the former is the sense of "we should do things the way we've previously done them" and the latter is "we should do things the most conservative way out of all of our options, even if we've never done it that way before."
NASA during Challenger would have been an example of the former [1]. In a way that I think many overly bureaucratic organizations are.
The other sense is somewhat oxymoronic given that conservatism is generally resistance to change. So when safety situations arise where the safest option requires acting novelly, who is there to lead the charge? I suppose in that case you'd want a radical safety department.
[1] From the NYT article on the findings of the Challenger commission, "As Commissioner Feynman observed, the decision-making was 'a kind of Russian roulette. . . . (The shuttle) flies (with O-ring erosion) and nothing happens. Then it is suggested, therefore, that the risk is no longer so high for the next flights. We can lower our standards a little bit because we got away with it last time. . . . You got away with it, but it shouldn't be done over and over again like that.'" http://www.nytimes.com/1986/06/10/science/shuttle-findings-l...