You can only "execute" people who get caught plotting against you and I guess, your dynasty, in a severe manner. Every other killing is an "assassination". One is (lawful?) execution of traitors, the other is murder. It might not be possible to murder people in the open arbitrarily, every murder is clandestine by default. Although you might not care whether you’re caught.
I think it is likely that to plot the demise of the ruler's wife earns an execution more readily than a plot for a promotion to chancellor. On the other hand, plots seem to be backed by force (give me the position or I march on your castle!), so you might get away with execution there too.
Another idea: Imprisoning somebody could result in a plot to free him.