If you are divorced, you are no longer married. You went through divorce proceedings, and your marriage no longer exists.
If you are legally separated, you went before the court to request that your separation from your spouse is legally recorded. It's a step past just separating and no longer living together. Legally separated is more formal.
To use filing status - married filing jointly - the couple MUST be married at the end of the year. They don't necessarily have to be living together.
IF you are divorced by the end of a tax year - then your correct filing status is Single OR if you have qualifying children - Head of Household
IF married persons are NOT living together they can still file jointly UNLESS they are legally separated. (Meaning there is a decree of divorce or separate maintenance (as of the last day of the year). It gets a little dicey if you are separated under an interlocutory decree of divorce - then your are considered married till it's final.
Basically Legally Separated means you have gone before a judge and you're almost divorced but not quite.
Look at the filing instructions for the F1040 - under filing status.