Minimal
I personally see minimal design as a reaction to complex design. For me, it is a style of execution. If you compare 2001 Yahoo with the modern-day Google search engine you can understand minimal (both are simple ideas). The minimal style does have some resonating qualities with “simple” which is where the confusion occurs.
The first use of the term Minimal was Post WWII. It influenced multiple disciplines and was a reaction to the styles at the time (as well as industrialization etc). The main idea was to do away with frivolous ornamentation and to convey clean, practical products that were inherent “well designed.”
Although the Art movements have more than moved on (to Post Modernism & Post Post Modernism), “Minimal” still plays an enormous role in modern-day Design.
Simple
We all know that the best ideas are simple. Unfortunately, 99% of client ideas are not simple (or at least the combination of ideas amounts to a complex brief). In my opinion, simplicity is a mindset. Any good designer worth their salt will constantly be asking:
“What is the simplest way I can convey this idea?”
And why is this? Complex executions often give you more information, increased functionality and sometimes a higher level of customization. How can these things be bad? However, the Achilles heel of the complex design is that they take a long time for the user to consume/learn/understand. If you consider the modern user’s attention span, presenting them with a complex layout is not the way to go.
Complex executions often occur from poorly considered, or rushed executions. A simple design requires a greater understanding of the brief, finding the core aspects of the idea and presenting the user with only what they need when they need it.
Simple vs Minimal
Refining a complex idea into a simple execution is always the ongoing task of the designer. This doesn’t mean the execution has to be minimal. Simple on mobile may mean using a “draw” to hide all of the menu options or using gestures instead of buttons to navigate. Minimal on the other hand may mean you choose to present a single piece of information on the screen at one time or choose to display images at full screen.
Simple design is often overlooked. This is because it simply works. It has been thought out and structured in a way that acknowledges eye navigation, visual hierarchy, information architecture etc. A simple design is easy to consume.
Although simple and minimal are not the same things they often work hand in hand with one another. For forward-facing systems executing your idea in a simple way gets your message across. In the end that’s the most important thing, a designer can do.