What is really happening when raster data is projected or reprojected?

[HalUshka]

This question is not specific to ArcGIS but rather is a general GIS question: what exactly happens when raster data, say for example a geotiff, is reprojected? I know from using the project raster tool that the raster cell coordinates change and, depending on the projection, the cells are rotated. Is anything else happening, or does reprojection basically just assign new coordinates to the raster cells? The project raster tool requires a resampling method as an input. Is this only used when the cell size of the output raster is different than the input raster, or is there always resampling upon reprojection?

Thanks in advance for your help, I dislike not understanding exactly how the tools I use work.

[NeilAyres]

There will always be resampling when re-projecting a raster image.

This is because of shape changes between one type of projection with another.

As far as I understand it, the raster is "moved" into the new coordinates, and a pixel center point grid in the new coordinates laid on top.

This then resamples the original by whatever method you have chosen.

Usually, nearest neighbor for discreet data, or some form of interpolation for continuous data.

This then means that if you have a histogram of the data distributions before and after, they will never be quite the same. Some data will always be changed, even if it is only by a small amount.