Regret - noun - feeling of loss or sorrow
Mistake - noun - error in judgment, action, or belief
For me personally, there is a huge difference between the two words. I've made many mistakes that I do not regret, and many regrets that weren't mistakes. I feel no loss or sorrow for myself, but I did make some errors in judgement. Oh well, life goes on. Live and learn and all that. No remorse :)