Every infection is intracelluar- virus have no own metabolism
Viruses briefly enter cells to replicate, but within a day or so they will have completed their replicate cycle, and have produced tens of thousands of copies of themselves — copies which then burst out of the cell by lysis, and enter the interstitial fluids and bloodstream. That then kills the cell. That's a normal viral infection, which termed a productive viral infection.
However, the same virus can also in some circumstances live long-term inside cells for years as a chronic intracellular infection which does not kill the cell. This is a very different type of viral infection.
Numerous studies have found such intracellular enterovirus infections in the muscles, brains and intestinal tissues of ME/CFS patients.