Yes, canonization is basically a 4 step process:
- Servant of God
- Venerable
- Blessed
- Saint
And different steps in this process give different privileges. For example, St. Thomas Aquinas (1225-1274) is a saint, and his feast day can be celebrated everywhere. But Duns Scotus (1266-1308) is a Blessed, and his feast day may only be celebrated in Cologne. (This is rather simplified).
The life and all the writings of the potential saint are investigated, and some miracles attributed to their intercession is also necessary to advance the process. It is the Pope who declares saints.
However, this rather tedious process is rather new. Historically, bishops had the authority to declare saints. For example, my country's patron saint, St. Olaf (995-1030) was canonized by the local bishop only a year after his death. If an old and genuine devotion to a local saint can be proven, then the Pope might give it his seal of approval years if not centuries later. This happened to Iceland's patron saint, St. Thorlak (1133-1193): he has always been honored as a saint by the Icelanders, and was formally recognised as a saint by the Pope only in 1984.
Also, many early saints were never formally canonized; the faithful just sorta understood that they were in heaven. These include Mary the Mother of God, all of the Apostles, St. Joseph, St. John the Baptist, etc.
A saint in this sense is a person who is in heaven. But the people we honour as saints (prayers, feast days, other devotions), have also show exceptional virtue and are worth imitating.
