Simple is that ‘horse that left the barn’ but remains in your line of sight. Chase her down and the problem is solved. Apply best practices in horse management to ensure it doesn’t happen again.
Complicated is trickier. It’s that feeling of being ‘caught between a rock and a hard place.’ You’re aware of being unaware of how to get out. Nevertheless, you are confident that good survival practices will help navigate you out of this mess soon enough.
Complexity grows each second you ‘grab the bull by the horns.’ Your best bet is to try things, getting a sense for what works and repeat. If you succeed in taming the wild beast, remember to reflect on your experience, teasing out useful knowledge that will help you repeat this success in the future.
We hear these idioms everyday because we encounter these types of problems everyday. Understanding the category of problem we are solving is the first step towards effectively solving it.
The really interesting part is to get better at ordering complex problems, thereby diminishing their complexity, or increasing the order of complicated ones so they become simpler.