首都 is literally the capital city. On the other hand, 都 is somewhat tricky. When we read the word as みやこ, it means the place where the Japanese emperor lived and lives, so it might be 京都, 東京, or perhaps 奈良. It's up to contexts or adjectives. However, when we read it as と, then it turns into the abbreviation of 東京都, like D.C.