[mesmark]

"The crying baby is getting on my nerves."

in this case 'crying' is functioning as an adjective. It isn't necessarily describing what the baby is doing now. In this case it creates inclusion. We're associating this baby with other 'crying babies' to create a feeling about the baby. It just so happens that this baby is crying now. (compare to 'Crying babies get on my nerves.')

"The baby crying (over there) is so cute when she giggles."

This places more emphasis on the action, or on what the baby is doing in order to define it or separate it from a group of babies or confusion with other babies.

Either way it sounds a bit funny. We use relative clauses to define something. 'swimming' 'crying' ... aren't very descriptive alone. In general, we tend to string more words together than that.

the boy scratching vs. the boy scratching his head
the girl swimming vs. the girl swimming with her friends

I hope that helps.