What is the difference between a Software Engineer that makes $100,000/yr and $400,000/yr?

Not that I'm assuming you are, but people tend to get too caught up in purely one dimensional numbers like salary. 

The only difference we can infer given the assumption is that one engineer has the power of convincing a company that he will provide enough value to be compensated $400,000, while the other $100,000.

There are many factors that can lead to that and we should not judge people too soon, solely by how much they make.

Even at the level of purely net worth, I may be happy taking $100,000 with lower taxes, working 30 hours a week in Austin, more freedom and flexibility, more tax efficient stock options, and lower cost of living. The $400,000 engineer could be in the Bay Area, working a stressful 80+ hours a week, with taxes at ~50%, no tax efficient stock options, much higher cost of living and such. I would say the quality of life of the first engineer would likely be significantly better than the second one, and in this case, the first engineer would be much better off.

Even though that's just one example, it illustrates the importance of evaluating a software engineer in a multidimensional fashion.

Now to answer your question in terms of what we could induce:

The $400,000 software engineer could likely have more experience, more managerial qualifications (e.g. CTO position) or specific specializations that are more valuable, such as a PhD in machine learning to AI algorithms.

Or the engineer could also be an expert in sales, negotiation and marketing to be able to convince someone to pay $400,000 a year.

My final piece of advice would be to not care about the salary as a main concern if it's above a living wage. People tend to be optimally happy at $70,000/year in the US. Making more is nice, but doesn't necessarily guarantees more happiness in terms of utility.

Work in a company you believe in and cares about you. Investing in yourself is usually the best investment you can make. Nothing cannot take that away. Even if you go bankrupt.

That's how I became a millionaire and more importantly, happy in life. The more short-sighted one is on just salary, the less likely they will be happy in life.