Long-term coexistence between cyanobacteria and their lytic viruses (cyanophages) in the oceans is thought to be due to the presence of sensitive cells in which cyanophages reproduce, ultimately killing the cell, while other cyanobacteria survive due to resistance to infection. Here we investigated resistance strategies in naturally resistant cyanobacteria and compared strategies against generalist and specialist cyanophages. Resistance was extracellular in most interactions against specialist cyanophages, preventing entry into the cell. In contrast, resistance was intracellular in practically all interactions against generalist cyanophages. Intriguingly, the stage of intracellular arrest was interaction-specific, halting at various stages of the infection cycle. These findings unveil a heavy cost of promiscuous entry of generalist phages into non-host cells that is rarely paid by specialists, potential unknown mechanisms of intracellular resistance and that the range for viral-mediated horizontal gene transfer extends much beyond just hosts.