Izuku is a spiderman AU. Quirks still exist in this but class 1a are not official heroes. Nobody knows about Izuku's identity, but when he saves Katsuki, will it come to light? Bakugo is hopeless romantic. 
Izuku got his spider abilities when he was bit by a spider and hides his identity behind a costume while saving people, he's loved by the public but they're weary of him at the same time

Katsuki Bakugou does not k n ow that Izuku is the masked vigilante unless it is stated so during the chat