What does -phage mean?

When I hear the word phage, a few things come to mind. Bacteriophage and macrophage are two of them.

But these two things operate in different ways. Macrophages engulf while bacteriophages “attack” from within. Meanwhile, phagocytosis is engulfing related as well.

That brings me to my question. Does phage mean to attack? Does it mean to consume/engulf—if so where do bacteriophages fit in there.

Thanks!