Based on a true story vs. "inspired by"...

Thoughts on historical fiction that is “inspired by” vs. “based on a true story”? For example, is it okay to fictionalize the name of a person in history (in this case a woman who made an important medical discover in the 1800s) and write a story that parallels her own, yet is not an exact retelling of her life?

Or do you recommend sticking more closely to the facts and perhaps modifying it a bit —then adding an author's note explaining what I changed?