I have the game set on manual training. Owner/trainer mode.
The GREEN bar is the current short term condition of your horse. It always drops the day after a race, and recovers fairly quickly. Sometimes it can recover within 24 hours, but rarely. Usually takes 4 to 7 days to return to full condition.
The RED vertical bar bolted onto the left side of the GREEN, is more long term condition for the season. It seems to be connected to the horses constitution level (horizontal GREEN bar in the right hand collection of horse characteristics). If the horse has a low constitution level, the RED vertical condition bar will drop far more quickly and will only recover with the horse having some BLUE time off (in the manual training function.

).
If the RED vertical condition bar drops dangerously low, the horse can incur serious injury and even die.
One of the key factors I look for in any horse, whether homebred, or bought from an auction, is a higher constitution level which means it can take more training and racing in any one season. If I have bred one with a very low constitution level, I don't even bother keeping it, just retire it from the game at the next annual update (10th April each year).
It's all really about juggling the many different parameters, and took me some time and frustration to work out simply through trial and error. If you really want to get into the game, you need to get to grips with so many different training functions. You'll get there eventually if you want to do it.
Clearer now?

Oh and, good luck!