What is the difference between a Croat and a Croatian or a Serb and a Serbian?

Answer 1

Croat, Serb, and Bosniak are ethnoreligious terms. A Croat is a Catholic Christian Yugoslav person or their children (if their descendants are not Catholics themselves). A Serb is an Orthodox Christian Yugoslav person or their children (if their descendants are not Orthodox themselves). A Bosniak is a Muslim Yugoslav person or their children (if their descendants are not Muslims themselves).

Conversely, Croatian, Serbian, and Bosnian are national terms that apply to citizenship. A Croatian is a citizen of the Republic of Croatia, a Serbian is a citizen of the Republic of Serbia, and a Bosnian is a citizen of Bosnia and Herzegovina.

As a result, you can have Croatian Serbs, who are ethnic Serbs who are citizens of Croatia, or Bosnian Croats, who are ethnic Croats who are citizens of Bosnia and Herzegovina, or Serbian Bosniaks, who are ethnic Bosniaks who are citizens of Serbia. Of course, the largest populations (pluralities or majorities) line up between the national and ethnoreligious terms, e.g. Croatian Croats, Serbian Serbs, and Bosnian Bosniaks.

Answer 2

The words Serb and Croat can only be used as nouns, whereas the words Serbian and Croatian can be used both as nouns and as adjectives. When used as adjectives, they can be used indifferently to describe a cultural or political phenomenon. Thus one can talk about a "Serbian church" located in Croatia and attended by Serbs.