In any theory, including philosophical theories, it is not the name of things that matters but their connections to each other and to our experience. Obviously we try to describe our theories in ways that are suggestive, but ultimately the names are irrelevant (a rose by any other name …). For example, consider “representation”. Obviously “representation” has an ordinary meaning in which it designates a particular kind or relation between two things. And it is possible to use the word representation in its ordinary sense in the context of a philosophical theory. But if the relationship of representation is important to the theory usually it will be explicitly defined, by giving conditions for when it does and doesn’t hold. So defined it becomes basically irrelevant that it is called “representation”, what matter is when it does and doesn’t hold, the conditions that define the relation in the context of the theory.
It is possible then for the same philosophical theory to be described with completely different terminology. In a trivial sense this happens all the time, when philosophy is translated from one language to another. But, more interestingly, it can happen without anyone being aware of the fact. This can happen when two originally distinct theories are slowly modified in response to objections and, as a result, end up being basically the same theory in content, but described with different words. And of course since they have gotten to this point by different routes it is usually not immediately obvious that they are the same theory.
This is best illustrated by an example. Phenomenalism (also known as idealism) is a philosophical theory, which, in its simplest version, holds that the external world consists of nothing more than our perceptions of it. Thus phenomenalism is a rejection of the existence of an underlying reality that is a source of those perceptions. Of course there are a couple obvious problems with phenomenalism. One is that it fails to explain the consistency of our perceptions, why a particular part of the world appears basically the same way to us between periods of observing it, and why that part of the world appears the same way to different people. One, relatively absurd, solution this problem is Berkley’s, which is to say that god is always observing everything and keeping it fixed. That is not a response available to modern philosophers of course, since invoking god to explain something is like invoking magic to explain something, both are basically unbounded by any restrictions and so can explain anything, but by being able to explain everything they are good explanations of nothing. Thus modern phenomenalists often invoke the idea of possible perceptions. These possible perceptions sit around dormant (I suppose) and trigger a certain perception whenever the perceiver is in the right state. This accounts for the observed consistency. And, to answer certain other objections, such possible perceptions are allowed to change over time in law-governed ways.
Now let’s consider indirect realism. Indirect realism holds that are perceptions are constituted by sense data. Sense data are generated by an underlying reality in a systematic way, so that usually the same real states of affairs give rise to the same sense data. However, the process is not infallible, sometimes we have sense data that are not brought about by their usual causes. And indirect realism holds that the underlying reality does not have the properties that our sense data seem to ascribe to it; while sense data reliably give us information about reality it is not the case that reality is fundamentally composed of colors, sounds, etc.
Now phenomenalism and indirect realism seem diametrically opposed. Phenomenalism is a kind of denial that there is anything more to reality than what we perceive of it, while indirect realism holds that most of reality is outside of perception, and that perception is simply our imprecise way of having access to it. But if we look beyond the names it is clear that the version of phenomenalism described here and indirect realism are really basically the same theory. The underlying reality of indirect realism is the possible perceptions of phenomenalism. And having certain sense data becomes another way of saying that we are perceiving something. Admittedly there still might be a small difference between the two theories in the way they handle error, but clearly they are more alike than they are different. The major differences are really in the way they are presented, phenomenalism is presented with an emphasis on the idea that there is nothing more to reality than perceptions (conveniently sweeping under the rug whatever other bits are needed to make it work), while indirect realism is presented with an emphasis on the that reality is not as we perceive it to be.
Of course phenomenalism and indirect realism are not the only philosophical theories that it is possible to merge. Often seeing that they can be merged is the hardest part, since sometimes theories that could be merged will use the same terminology to describe different things; since we tend to mentally “line up” different theories by where they use the same terminology this can make seeing the underlying similarities that much harder. One sign that it may be possible to merge two theories is that they explain the same things and have the same explanatory virtues and faults. Additionally, diagramming the structure of the theory and the relationships of the theoretical entities can also visually reveal similarities in structure, which may indicate the possibility of merging them. But, like most things there is no completely infallible way to detect theories that might be merged, except by trying out various possible ways of merging them and seeing if any work.