If you consider the closest star to us is over 4 light years away. The sun and that star are single grains of sand on a football field flying at each other. Chances they are going to hit is very, very small. You can fit every single planet in our solar system in-between Earth and our moon. Space is huge.

The chances 2 stars will ever collide is miniscule. What is will happen much more readily is stars passing each other and getting redirected by their gravity wells and flung off.

If they were to collide, there are so many factors to consider there isn't a one answer fits all. A giant red and a white dwarf are going to react much differently than 2 heavy neutron stars. It probably goes from one absorbing the other to forming a black holes or super novas or one stripping the other or fragmenting into masses which form new stars.