The difference is that in practice, most "pro-capitalism" individuals are actually okay with the state taking on a wide variety of tasks on some level: military, police, roads, public schools, environmental regulations, labor and health codes, zoning, etc. Sure, GOP-controlled (or your local right-wing equivalent) areas tend to have less of these things, but less isn't the same thing as none.

In contrast, anarchists are usually opposed to having any state whatsoever. The ideology tends towards being far more extreme and uncompromising.