These two questions are much more similar that we tend to assume, despite the normative/positive distinction emphasized in EC101 textbooks.
They are not identical questions in the short run---say the October or December Fed meetings---but over a long period of time they are pretty much the same question.
To see why, start with the thought experiment that the Fed had a 2% inflation target, or a 4% NGDP growth target, and used a futures market to implement its policies. If they pegged the prices of CPI futures along a 2% inflation rate, then the money supply and interest rates would be completely endogenous---controlled by the market, not the Fed. Interest rates both would and should adjust along the path required to keep inflation expectations at 2%.
Even under the current policy regime, where there is a bit more discretion, there is actually far less discretion than most people assume. The Fed had originally planned to raise interest rates in mid-2015. They also wanted to raise interest rates in mid-2015. Why didn't they? Because the markets began telling them that a rate rise was inconsistent with their macro goals, especially 2% inflation.
That's not to say that the Fed has no discretion. They are free to make mistakes in the very short run. (That's what discretion means, freedom to make mistakes.) They are free to set rates at a level that will cause inflation to diverge from the target. But if they want to avoid a macroeconomic disaster (and they do, even the ECB does) then they need to quickly "make-up" any error with future rate settings.
Here's another way of making my point. I argued against a rate increase in September, and will probably argue against one in December. If it turns out that 2 or 3 years from now the Fed is setting rates where the Fed currently expects to set rates, then I will have to concede that my current views are wrong, and that a rate increase in December would have been called for.
In contrast, if 2 or 3 years out in the future the Fed is setting rates where the market currently thinks they will be setting rates, then the Fed hawks (and even some doves) that now favor a rate increase in December will have clearly been wrong.
What discourages me most is not that people are right or wrong (there's a good chance my views will turn out to be wrong.) Rather what discourages me most is that people don't seem to even understand that after the fact it is possible to ascertain who was right and who was wrong about monetary policy. For instance, in retrospect Richard Fisher was clearly wrong in advocating a rise in interest rates in July 2008. In retrospect the Fed was wrong to not cut rates in September 2008 (as Bernanke acknowledges in his book.) But we actually know far more than that. We know that the Fed set rates too high throughout late 2008. We know that the Fed hawks have been consistently wrong since 2008, every single time they disagreed with Fed policy. And I mean consistently wrong, not right once during a single debate in the past 7 years. Not once. But I don't see the hawks acknowledging that fact.
There seems to be this weird view that even after the fact, "Who can say?" who was right and who was wrong about policy. But that's not how the world works. If you want to be even close to 2% inflation you need to set rates at a level that leads to that outcome. The market determines the path over any extended period of time, even if the Fed can deviate for a few meetings. The market eventually tells us who was right and who was wrong, it's not "debatable".
Of course the policy target itself is debatable. I prefer NGDP targeting to inflation targeting. But as long as the Fed has an official agreed upon 2% inflation target, they have to eventually set interest rates where the market tells them. They wanted to raise rates last summer, and the markets said no. They currently want to raise rates to 3.5% over the next few years, and I suspect the markets will again say no. If I'm wrong and rates do rise that much, then the markets and I will have been wrong. I will have no right to say, "Yes they raised rates to 3.5%, but they should not have." They have some discretion, but not that much. If they are even close to that level then I will have been wrong.
PS. I hope after reading this post you understand how idiotic it is to complain that the Fed's been running a "low interest rate policy". Nonsense. They have a 2% inflation target, and the markets decided that this target requires low interest rates. When the ECB tried to fight the market in 2011, and raise rates, the were brutally rebuffed, and now eurozone savers face years or even decades of near zero rates, as punishment for the ECB daring to defy the Credit Market Gods.