For documentation I would recommend the OLCI ATBDs which are accessible from the S3-OLCI Document library
Here you find the "Sentinel-3 OLCI Atmospheric corrections over Case 1 Waters ATBD" and the "Sentinel-3 OLCI Bright Waters Atmospheric Correction ATBD" which together describe the standard AC, i.e. the water leaving reflectances that are included in OLCI L2 Water products are generated according to these algorithms.
In the document library you also find the "Sentinel-3 OLCI Alternative Atmospheric Correction ATBD". This is an alternative which is internally used by the ground segment processor to generate water leaving reflectances which are used to retrieve the concentrations in Case 2 waters, i.e. input to the neural net. However, these water leaving reflectances are not written into the OLCI L2 water product distributed by ESA & EUMETSAT
The ground segment Level 2 processing and C2RCC processing (using default settings) are basically the same. There are preprocessing steps, like the smile correction, or the gaseous absorption correction, which can be different. However, the neural nets used in the ground are exactly the same as the ones in C2RCC, and also the processing logic and thresholds used by the two different processors are the same.
Of course, the C2RCC processor allows you to modify the default setting of many processing parameters, like the conversion from IOP to concentrations, or the thresholds used for flagging. Also, the C2RCC allows output of variables not available in the ground segment. When choosing non-defaults you get different result than the ground segment products.
I hope this helps!