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Four Ways to Study Science

The word "science", as we use it, has two primary meanings:

(Process) A cyclical process of thinking and observing that conforms to a certain method which, nominally, allows us to discover truths about the world.
(Institution) The activities performed by the institutions nominally responsible for the above, insofar as they are thought to pertain to the above process.

When we make a claim about whether scientists can be trusted, or whether science in general is working, we are almost always using the word "science" in the second sense, not the first. This distinction between science qua process and science qua institution is roughly a distinction between idea and implementation, between map and territory.

Hence, there are no less than two possible ways in which we can discuss science: as process, and as institution. These are the same, however, in their being a way to achieve a goal. The goal of the process is to understand the external world, and the goal of the institution is to guide humans towards performing the process. For any method of achieving a goal, we may ask no less than questions about its relation to its goal:

(Nature) How is it even possible to achieve the goal via this method? What aspect of the method allows it to achieve the goal?
(Improvement) What does this method look like when it is best achieving its goal, and how can the deficiencies of any implementation of the method be diagnosed and repaired?

Two questions times two methods gives us four ways to study science:

Nature of the process. How can science tell us anything about the external world? The area which tackles this is analytic philosophy.
Nature of the institution. How can the process of science even be performed by humans? The area which tackles this is philosophy of science$^1$.
Improvement of the institution. How can any given scientific institution be made better? I do not know if the area which tackles this has a commonly accepted name, but the wiki page on metascience is basically just this, so I'll call it metascience as well. There are several initiatives in this area, such as Guzey et al.'s New Science, which explicitly "aims to build new institutions of basic science".
Improvement of the process. How can the cyclical process of thinking and observing that we call science be done more effectively by any given scientist? Again, I do not know of a name for this area, so I'm calling it metacognitive science. (Pattern-matching according to the table below would give the name meta-analysis, but that's incredibly vague).

$$ \begin{array}{|c|c|c|}\hline {\color{gray}\downarrow \ of\ the \ \rightarrow} & \textbf{Institution} & \textbf{Process} \\\hline \textbf{Nature} & \text{Philosophy of Science}&\text{Analytic Philosophy} \\ \hline \textbf{Improvement} &\text{Metascience} & \text{Metacognitive Science} \\ \hline\end{array} $$