Is dark matter inside galaxies different from dark matter in intergalactic space?

The standard model of cosmology (for now) is called Lambda-Cold-Dark-Matter. It has only one kind of dark matter, and it agrees well with the observational data.

Other types of dark matter, such as “warm” or “hot” rather than “cold”, have been considered, and some people have considered models in which more than one kind of dark matter exist. These more complicated models do not appear to be necessary to explain what we observe.

The precise nature of dark matter doesn’t matter in cosmology. What matters is the relationship between its energy density and its pressure, because in General Relativity both energy density and pressure cause gravity. What is important is how relativistic dark matter is, because that determines its pressure. Cold dark matter is non-relativistic and has negligible pressure. All of its gravity comes from its energy density.

Others have made the point that the current concordance cosmology includes only one variety of dark matter, which is cold. This is correct.

If dark matter is indeed some as-yet unknown particle, it would be surprising if it was the only unknown particle. The standard model of particle physics is basically complete, without room for extra particles without changing some of the underlying principles. There are some anomalies which point to our knowledge of particle physics being incomplete, so eventually discoveries will likely be made. Anyway, all this is to say that there are probably many species of dark particles, but it is currently thought (mostly by invocation of Occam's razor) that the 'astrophysical dark matter', the stuff that explains the motions within and between galaxies, is either predominantly due to one particle, or a family of particles which behave similarly as far as the relevant astrophysics is concerned.

Now I hesitate to make this next point in this way, but I think there is some merit to the statement that dark matter isn't "the same" on all scales. The standard cold dark matter has been hugely successful in explaining the physics of the large scale Universe, but fails in some areas on small scales. There are other examples of ideas to explain astrophysical dark matter which work very well on small scales but struggle on large scales. One example is the modified gravity theory MOND. I bring up this particular theory only because there is a nice, reasonably accessible article contrasting it and LCDM available here:

As yet no one theory has succeeded in explaining the dark matter effect on all scales, which is why we still have an astrophysical dark matter problem, in addition to the question of what particle dark matter might be.

So I agree with some interpretation of (the spirit of?) the statement, but I don't think it was especially well articulated in the article cited in the question.