By size, the Solar System has 4 Mercury-sized bodies: Mercury, Ganymede and Callisto (the 2 bigger of the 4 big satellites of Jupiter), and Titan (satellite of Saturn).
There are also 4 Moon-sized bodies: the Moon, Io and Europa (the 2 smaller of the 4 big satellites of Jupiter), and Triton (satellite of Neptune).
Pluto is smaller than Triton, but not much smaller. It is the next in size after these bodies and it could be considered to belong to the same size class as the Moon-sized bodies, because the next smaller bodies are significantly smaller. While Pluto is not a satellite of Neptune, like the satellites it does not have an independent movement, but one that is connected to the movement of Neptune through an orbital resonance.
You are right, Eris is close enough in size to Pluto and to the other 4 Moon-sized objects to be considered in the same class size.
In the past, for a long time the uncertainties about the sizes of Pluto and of Eris were great, so it was not clear how close in size they are to the other much better known Moon-sized bodies.
There are also 4 Moon-sized bodies: the Moon, Io and Europa (the 2 smaller of the 4 big satellites of Jupiter), and Triton (satellite of Neptune).
Pluto is smaller than Triton, but not much smaller. It is the next in size after these bodies and it could be considered to belong to the same size class as the Moon-sized bodies, because the next smaller bodies are significantly smaller. While Pluto is not a satellite of Neptune, like the satellites it does not have an independent movement, but one that is connected to the movement of Neptune through an orbital resonance.