I have often been asked by people "so do you work out?".
If you are just a recreational athlete or weekend warrior, this statement may not make much difference to you. After all a "training session" is legitimately called a "workout" in real strength & conditioning circles.
But the implications of these two words are very far apart.
"Working out" has a connotation of expending energy, making your body tired physically. Probably it also means maxing out in the training session. The goal of "working out" is the session itself.
On the other hand, "training" has a connotation of working for a long term goal. The goal of a "training session" is maybe months or years away.
When somebody is going for a competition, you don't ask "what do you workout for?". You ask "what are you training for?".
For me i am training. Every training session is bringing me closer to my goal, no matter how far away it is. I don't workout to "keep fit". I started with a lousy level of performance. If i were to "keep fit" my performance would still be pathetic. I don't want to "keep fit". I want to be more fit for my goal.
So are you training or are you working out? Are you going for higher levels of health & fitness or are you "keeping fit"?