They used to have "Serbo-Croatian" as the official language of Yugoslavia. There was a joke that only the Jews use it. Two former israeli chief of staffs were native serbo-croatian speakers.
The differences between Serbian and Croatian are obvious to any native speaker of either language:
1) Modern Croatian uses the Latin alphabet. Serbian uses the Cyrillic script in most cases.
2) Standard Croatian is jekavian: djevojka, svijet, bijesan, uvijek.
Standard Serbian is ekavian: devojka, svet, besan, uvek.
3) Consider the following sentences:
English: The train will leave the railway station at ten o'clock sharp.
Croatian: Vlak sa željezničkog kolodvora krenut će točno u deset sati.
Serbian: Voz sa železničke stanice krenuće tačno u deset časova.