Yes, there are many differences.
However, it's sometimes trickier.
Challenger blew up in full view at launch while Columbia burned into pieces on the way back.
This meant that the Challenger 7 never experienced what they had been trained for while the Columbia 7 enjoyed their 16 days in space to the fullest.
But it also means the Challenger tragedy was a lot easier to fix as the "smoking gun" appeared very quickly.
The Columbia tragedy may never completely be solved and therefore any fixing might involve more guessing than confident explanations.

There have been debris falling from the ET at every shuttle launch. Does that mean that this time it hit a particular place at a particular angle and a particular speed? Does that mean there's a one out of 113 chances that it will do so?
The debris did not hit the leading edge of the wings (where the heat is maximum) otherwise the astronauts would have seen it. So it hit the bottom of the Shuttle and perhaps near the wheel well.

But it might be something that happened later on, in space.

There may be no way anybody can be blamed for a specific mistake and this will make it harder to fix. It will also render the Shuttle much more dangerous than we thought as statistics show up.

The only way out is by relying on different systems, (like the shuttle and a manned capsule to go up to and come down from the ISS) but any way out will be expensive.

I'm curious about what decision will be made: build another Shuttle or build a much smaller capsule or lifting body only meant to carry humans (a whole serie of them).

Raoul