They were separate races.
They both ran together from when the ToB (current version) started in 1987 until the Milk Race ended in 1993.
The Milk Race was about 11-12 stages, and was a top end amatuer race (incl Russian etc national teams plus some lower end Pro teams).
The ToB was initially 5 stages, growing to 8 currently, had a dodgy spell with only 2 races between 1994 & 2004, but has always been a proper Pro race with proper Pro teams.
The first race I went to watch was the Milk Race, going up Winnats in I think 1986. The back end of the race were pushing.