Good questions.
The difference between a road bike and a cyclocross bike have been discussed before in
this thread an in
this thread .
In essence, a cyclocross bike is a very specialized road bike adapted to challenging off-road conditions. It is possible to ride a road bike off-road, but it would never be a true 'cross bike for a few reasons:
1. Few road bike frames give enough clearance for wide and knobby 'cross tires.
2. Few road bike frames are equipped with cantilever brakes, and can't normally be retrofitted without having modifications made to the frame.
3. Most road bikes have a more agressive geometry than a 'cross bike; you'd probably find one a bit sketchy off-road.
Your options would be to buy two bikes [not such a bad thing], to buy a cyclocross bike and use it on the road with skinny road tires [I have a friend who does that, and I sometimes use my 'cross bike on the road in bad weather], buy a touring bike and use it for 'cross in the winter [touring bikes are similar, in many respects, to cross bikes].