I guess "forecast" is more explicit about the fact you're trying to guess what will happen in the future, so it's clearer that you can't be totally confident about when you'll finish.
If you say "I estimate 2 weeks", then the word "estimate" is often taken to mean "2 weeks, plus or minus 10%" (or some other fixed bound), when what you probably actually mean is "between 1 week and 6 months, but probably around 2 weeks".
If you say "I estimate 2 weeks", then the word "estimate" is often taken to mean "2 weeks, plus or minus 10%" (or some other fixed bound), when what you probably actually mean is "between 1 week and 6 months, but probably around 2 weeks".