Allah also mentions those who were given the Kitab 2:102, 2:121, 2:144-145, 3:19-3:23, 5:5, 9:29, 13:36, 74:31, 98:4, those who inherit the Kitab 35:32 and that this prophet (ie. Muhammad) was given the Kitab as well, 4:113, 5:48, 29:47.
From 2:109-113 it looks as though the Jews and Christians are from the Ahlul Kitab. Allah speaks of those among the Jews, Christians and Sabians who believe in Allah and the Last Day 2:62, 5:68-69. Would anyone believe in Allah and the Last Day without a kitab?