Macrophages play a role in both innate immunity and adaptive immunity.
In innate immunity, they phagocytise the pathogens and they also release cytokines that promote the recruitment of other immune cells to the site of infection. Some of these cells are Natural Killer cells and basophils but they don't start with M.
In adaptive immunity, Macrophages have the ability to breakdown the pathogen and find specific markers on the pathogens that can be used as a target by the adaptive immune response. This marker is called an antigen.
They then take the antigen and present it on a receptor called MHC Class 2. This MHC Class 2 basically holds the antigen while the Macrophage makes its way to a lymph node, where T Helper cells are located.
The T Helper cells can then analyse the antigen on the MHC and promote the proliferation of T and B cells which will specifically seek out that antigen in the body and destroy any cells that have that antigen present.
Here's a video of phagocytosis in action, its pretty cool that this stuff is just happening inside of us and we have no control over it.
https://www.youtube.com/watch?v=BlPlgGbb2IU&t=114