Difference between layout engine and javascript engine

After long readings, it seems that when people say the browser engine, they refer to a linking mechanism such as gecko or webkit.

I also know that the layout engine is mainly responsible for “drawing” the screen, and the javascript engine is used for interpretation.

The question, though, is for a modern web application that has a greater impact on performance? And how are these two connected? What are their other uses outside the browser. What other functions do they serve.

Many thanks.