They are pretty much interchangeable.
Student or Learner
First please look at the following two sentences:
From 50 000 to 500 000 people died in the accident.
Children aged between 7 and 11 will have to be accompanied by their parents.
I wonder if the "From ... to ..." in the former can be replaced by "Between ... and ..." and if the "Between ... and ..." in the latter can be replaced by "from ... to ...". If they are not interchangable in this case,are there any cases where they can be interchangeable? Any reply will be much appreciated.
They are interchangeable in both cases. To me, "between 50 000 and 500 000 people died in the accident" and "children aged from 7 to 11 will have to be accompanied by their parents" sound more natural, but nobody can say that your counter-examples are wrong.
I find "Between 50,000 and 500,000 people" much more natural in the first.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.