Hint: this has nothing to do with grammar

First, a way to think about the difference:
Something “complex” involves many things.
Something “complicated” involves extra things.
My computer, on which I’m writing this, is complex, as machines go. My computer crashing because I dropkicked it (don’t ask why I’d do that) would be a complication. Human relationships are generally complex, but nobody wants one that’s complicated. When we say something is complex, we usually mean it’s not straightforward. When we say it’s complicated, we typically mean it’s not working like we’d like it to.
Another way to think about it is, things we describe as complex have many parts, but all of them are necessary. Things we describe as complicated, on the other hand, have parts that are extra because they’re unnecessary, or unwanted.
And this isn’t just an exercise in grammar, either. It’s a critical difference that every leader, teacher or communicator needs to know (that’s everyone, in case you missed the hint).
So why does this matter?
The first thing is to understand two things:
Everything is complex, and everything can be simplified.
Yes, I mean everything.
The very chair you sit on consists of atoms spinning around randomly, and which only give you the illusion of stability because their spinning cancels out overall.
The ground under your feet is spinning at over 1600 km per hour, and hurtling round the sun at 30 km per second. But again, it feels stable because you’re moving right along with it.
Your simplest relationships are sustained by an intricate web of verbal and nonverbal signalling in every interaction, all of which you process to determine how to respond to each other and how to generate desired responses.
You get the picture. Everything is complex.
But everything can also be simplified. You simply sit on the chair. You walk like the earth isn’t moving. You categorise your relationships—parent, child, colleague, friend, best friend—each name a code for how you’re handle each one.
The second thing is to understand that one of the most important things we have to do is this work of simplifying. And simplifying is even more important when we have to get other people on board, whether as leaders, teachers or communicators.
(Remember, to simplify something isn’t the same as making it easy.)
If you lead, you want to simplify the vision (as well as the actions your people need to take based on it). If you are a teacher you want to simplify the concepts you want to impart. And if you are a communicator of any kind, you want to simplify your message, whatever that is.
Just how do you simplify, though? That’s where the difference comes in.
You simplify the complicated by pruning—removing the extras.
You simplify the complex by defining—getting to its core.
But if you don’t know which is which, you’ll definitely end up complicating things.
Faced with a situation, how them do you distinguish? I can’t help you much there (without knowing the exact situation) but one way is to deliberately ask yourself the question: what’s necessary here, and what’s extra?
And have the humility to understand that sometimes, like in relationships, or on a new job, you have to ask others.
A lot of what we might consider complications in other people or organisations are just part of their inherent complexity. But sometimes too, what they consider their inherent complexities are really complications.
Hey, this isn’t complicated, right?