The difference is that upon its expression evaluating to false, skipWhile changes over to mirroring its source observable – so it will cease to filter out any further values.
For example:
Observable.from([1,2,3,4,5])
.pipe(filter(val => val % 2 == 0)) // filters out odd numbers
.subscribe(val => console.log(val)); // emits 2,4
Observable.from([1,2,3,4,5])
.pipe(skipWhile(val => val % 2 == 1)) // filters odd numbers until an even number comes along
.subscribe(val => console.log(val)); // emits 2,3,4,5