Others in this thread already went into more details about this, but it doesn't help me much as long as I don't have an idea what the basic difference between both approaches is.
Can someone ELI5 the gist of both approaches?
TypeScript, on the other hand, has always set its goal to be a superset of JS and to transpile to JS only. This means a more familiar syntax, as well as (practical, IMO) design choices that ensure higher compatibility with the existing JS ecosystem. There is no TypeScript without JavaScript. Its development coincided with that of VSCode, and arguably is one the main facilitators for the latter's feasibility.
I have to say Microsoft's grand plan of VSCode and TypeScript has to be one of the most astonishing software revolution in this decade. The foresight and acuity of Erich Gamma and Anders Hejlsberg is just amazing.
One of his projects at Microsoft was J++ which is basically own-brand Java. Doubtless that's great material for learning to design C# but nobody is going to claim J++ was a success.
VM integration with host OS, J/Direct (P/Invoke), events, COM integration, WFC (Windows Forms).
TypeScript deliberately takes a "good enough" approach to improving JavaScript, instead of designing an ideal but incompatible approach. For example, its handling of function parameter bivariance (https://www.typescriptlang.org/docs/handbook/type-compatibil...) is unsound but works much better with the existing JavaScript ecosystem. By contrast, a more academic functional programming language would guarantee a sound type system but would be a huge shift from JavaScript.
By analogy, Herb Sutter is arguing that something like the C++ Core Guidelines (https://isocpp.github.io/CppCoreGuidelines/CppCoreGuidelines), with tooling help in this new Cpp2 syntax, can bring real improvements to safety. Something like Rust's borrow checker would bring much stricter guarantees, backed by academic research and careful design, but would be incompatible and a huge adjustment.