coordinate system - Distances in {Plate Carrée projection - EPSG:4326 - WGS84}

"4326 is just the EPSG identifier of WGS84" [3]

Indeed http://spatialreference.org/ref/epsg/4326/html/ says it is a GEOGraphic Coordinate System:

GEOGCS["WGS 84",
    DATUM["WGS_1984", 
        SPHEROID["WGS 84",6378137,298.257223563,AUTHORITY["EPSG","7030"]],
        AUTHORITY["EPSG","6326"]],
    PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],
    UNIT["degree",0.01745329251994328,AUTHORITY["EPSG","9122"]],
    AUTHORITY["EPSG","4326"]]

Citing [1], [...]

one of the most common ways the round world is displayed on a map is using the simplest projection we have:

x = longitude
y = latitude

The name of this projection is “Plate Carrée”, and is widely used because it is so simple. However we often seem to forget that we are talking about a projection. Therefore the spatial reference for this projection is very often (mis)referenced as a spherical coordinate system like for EPSG:4326.

In [1] then a correct WKT for the Plate Carée projection is reported (a projection is overlaid over WGS84/EPSG:4326):

PROJCS["World_Plate_Carree_Degrees",
    GEOGCS["GCS_WGS_1984", 
        DATUM["D_WGS_1984",SPHEROID["WGS_1984",6378137,298.257223563]], 

    PRIMEM["Greenwich",0],UNIT["Degree",0.017453292519943295]], 
    PROJECTION["Plate_Carree"],PARAMETER["False_Easting",0], 
    PARAMETER["False_Northing",0],PARAMETER["Central_Meridian",0], 
    UNIT["Degree",111319.49079327357264771338267056]]

which is ~EPSG:54001, except that units are not meters but degrees.

I am quite a bit confused for example if, at least in practice, EPSG:4326 is equivalent to Plate Carrée equirectangular projection.

E.g. in a computing environment, projected data is much more convenient since distances are Euclidean and not great-circles: would the distance between two points in EPSG:4326 be different then with respect to the same points in a Plate Carrée?

This is maybe specific to the single application, e.g. [2] Open Layers uses the term 'EPSG:4326' to mean the Plate Carrée projection. R seems to assume a spherical WGS84 instead (-> r-sig-geo).

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