Dart was made by Google as a new language for the web. In the beginning, it was already quite different from JavaScript at the time, and crucially the main way to use it is through the Dart VM (that was embedded into a build of Chromium). It did have compilation to JS, but AFAIK never caught on. In the end, Dart diverges from JS so much so that the split in ecosystem means it's not viable for the web anymore.

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.