"to work out" - to exercise, to train - I work out *at* home instead of going to the gym. "to work from home" - to work at home instead of at an office or other workplace - I have been working from home since the baby was born. I work out "from" home - I have not heard of this usage so if you could provide the source of your quote, I may be able to comment further.

Thank you everyone for answering my question!

Both sentences mean the exact same thing. However, the term work out can mean physically working out, gym. So in that case you would say, I work out at home. " AT" is needed to mean you are working out at your house, not from your house. You still would not say I work out from home to mean you "workout " as in doing gym work. So its tricky. So if you work out from home, or work from home, it means the exact same thing. A small percent of people will say work out from home, majority will just say work from home. But working out at home, is a different meaning, that is doing gym workout at home.

I work from home. ( if job related ) I workout at home. ( if exercise related )

I'm not a native, so maybe I'm not right, but to work out means to train (for example exercises with weights in the gym). So in this case I think "I work from home" is better.