Scripts for index images

I’m not familiar with JS, so want to clarify that NDVI and NDWI in the “Python scripts template” use the standard equations? I think I’ve also seen:
return [B8A - B05 / B8A - B05]

NDVI: (NIR - Red) / (NIR + Red)
Sentinel 2 - Band 8a (NIR) & Band 4 (R )
Landsat 8 - Band 5 (NIR) & Band 4 (R )

Sentinel 2 - Band 8a (NIR) & Band 11 (SWIR)
Landsat 8 – Band 5 (NIR) & Band 6 (SWIR)

Or is the below script (S2 NDVI) just ratios of the bands; values look correct for the downloaded S2 image? Can I similarly put the S2 band names for NDWI? Do similar scripts for L8?

let viz = new Identity();

function evaluatePixel(samples) {
let val = index(samples[0].B8A, samples[0].B04);
return viz.process(val);

function setup(ds) {
setInputComponents([ds.B04, ds.B8A]);

I am not sure, what your question is.
let val = index(samples[0].B8A, samples[0].B04);
is the same as
let val = (B8A-B04)/(B8A+B04);

You can find many configurations here:

Thanks Grega, you answered my question. If they are both same, why use the big script in the template? Or does the big script offer any advantages?

In this specific case, for simple indices, there is no reason to use the “big script”.
There are however more complicated cases, where the structure is required.
E.g. multi-temporal processing (cloudless mosaics):

or Leaf area index: