Software engineers develop or maintain software projects. Usually this involves writing code, but there are also jobs that are more about analysis, testing, operations, or monitoring.

There's effectively no difference between a software engineer and a software developer. Either title can be used for the same role, so it's more or less just whatever became traditional at a given employer. There are also other titles for virtually the same role, for example Programmer/Analyst.

What you need to learn includes things like the languages and frameworks in the MERN stack, but I've always thought the tools are less important than learning how to solve problems. This is harder to define. It's about learning to think about problems until you can break them down into steps that can be implemented in software. This thought process is very similar no matter what code language you use.

In fact, if you become a professional software engineer, you will use many different programming languages. Some people say you should learn a new language every year or two. So don't try to pick the "right" language to learn. Many are good choices and you can use any of them to practice the skill of solving business problems.

You mentioned Google. I have often recommend this article written by a Google leader Peter Norvig: https://www.norvig.com/21-days.html It's full of good advice for people like you, looking to enter the field.

Besides Google and Amazon, there are many other companies I'm sure you would find rewarding. Don't limit yourself to just the famous ones. You will have more opportunities if you broaden your search.