coordinate system - GEOTIFF explanation of .aux xml and tfw world file

I want to know how raster images work,

I have a set of geotiffs that has no aux, tfw or xml

when I check the spatial information in arccatalog, they do have an projection. and they shows correctly.

if the projection is embedded in the geotiff, why do I need .tfw ?

I need to know what it does, is it used for quick transformation if the geotiff is in real coordinates wgs84 and I want another projection for fast show? or does my geotiffs lack some information?

and when I define another projection, arccatalog creates aux, do i need to keep this aux?

so. shortening the question, what is aux, tfw good for if the information is already stored inside the geotiff?