What is the wine maturation stage that occurs just after bottling?

When you bottle do you add a yeast inhibitor like Camden / Potassium Metabisulfide? Or do you allow bottle conditioning to produce some carbonation? Both methods for still or carbonated wine have an impact on the finished flavor. Slightly more attenuated carbonation adds a little bite to flavor and dryer mouthfeel. Camden depletes oxygen to prevent further fermentaion, leaving it for the most part as the wine that is bottled but slightly smoother with the absence of O2 for a time.

My guess would be that when you bottle a little oxygen gets into the wine and over the next few days/weeks oxidation of the compounds in the wine reduces the 'roughness' and helps round it out. In a similar way that opening a bottle and letting it breath for 45min before drinking can improve a bottle.

Excessive oxidation will lead to vinegar, but a little can improve the wine, and help it develop. The cork in wine allows oxygen to slowly seep into the bottle over years and helps the flavours develop.

For some in depth analysis of wine oxidation this paper will provide all the information and citations to keep you going:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.467.6011&rep=rep1&type=pdf

Aging in the carboy or demijohn or whatever is called bulk aging.

Once it's bottled, it's called bottle aging.

As you have noticed, it's different, and primarily results from the volume of the container. Large containers age slower than smaller ones, however you want to bulk age so it's all aging together before you divide it out into individual bottles. Different things happen at different layers in bulk (I couldn't say what precisely), and so you want it to stay together so the wine can Move into and out of the regions slowly. Once it's bottled into a smaller bottle it's been sequestered from the rest of the batch and takes on a life of its own and each bottle will become slightly distinct from each other bottle due to how its treated, light, temp, etc. even if it's standing up or laying down.