They are not the same. EPSG:4326 refers to WGS 84 whereas EPSG:900913 refers to WGS84 Web Mercator. EPSG:4326 treats the earth as an ellipsoid while EPSG:900913 treats it as a sphere. This affects calculations done based on treating the map as a flat plane which is why your features got plotted on the wrong places.
The term 'projection' is often used as a synonym for the more correct term, coordinate reference system (CRS), which can include geographic and projected coordinate reference systems.
When a geographic CRS is displayed in two dimensions, its angular units are treated as if they are linear--they're just displayed. They are not displayed using a Mercator projection algorithm. The closest projection algorithm is Plate Carrée. Its forward equations are:
x (easting) = R*lambda (if the central meridian is zero)
y (northing) = R*phi
where
R = radius of the sphere (in your case the semimajor axis of WGS84 would be used)
lambda = longitude in radians
phi = latitude in radians
so you can see that true Plate Carrée coordinates are just scaled compared to displaying latitude-longitude values in degrees.
While the x equation is the same for the spherical Mercator equations, the y equation is different:
y = R ln tan (PI/4 + phi/2)
When you request data from an image-based web service like WMS, usually the layers have been cached (pre-built) in various CRS. The service then publishes which CRS are supported.
Note: Unfortunately, my company (Esri) is guilty of popularizing the usage of 'projection' instead of 'coordinate reference system'. I would just like to state that I started at Esri after that erroneous usage began.
Best Answer
4326 is just the EPSG identifier of WGS84.
WGS84 comprises a standard coordinate frame for the Earth, a datum/reference ellipsoid for raw altitude data.