Toast is used to mean "to brown, as bread or cheese, by exposure to heat". It is only slight cooking just enough to brown the outside. (such a bread is also called toast)
Roast means :
1. to bake (meat or other food) uncovered, especially in an oven.
2. to cook (meat or other food) by direct exposure to dry heat, as on a spit.
3. to brown, dry, or parch by exposure to heat, as coffee beans.
4. to cook or heat by embedding in hot coals, embers, etc.: to roast chestnuts.
While Toast is only slightly cooked, to roast is to cook either in an oven or open fire (often using hot coal or ember)