When pigeons coo the pigeon is communicating with other pigeons just like humans talk to each other by words the pigeons use the coo sounds to communicate and talk to other pigeons.
So when you hear pigeons cooing they are talking to and communicating with other pigeons in the area.
If the pigeon is constantly cooing all the time then the pigeon is likely calling for a mate or may be trying to attract another pigeon as a mate.
When the pigeon or pigeons are making a grunting noise, this grunting noise that pigeons make usually means they're in distress or they're using the sound as an alarm or to warn others.