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.

Both 都 and 首都 have same meaning : capital 都 is old-fashioned word. Usually in Japan, when using this word, it means Kyoto (former capital in Japan) And 首都 means capital or Tokyo (present capital in Japan)