Regional public transport is in Germany administrated by often smaller, local transport authorities (Verkehrsverbund) and there is no country wide tariff or ticketing system. It can be confusing enough for native Germans when visiting an unfamiliar place to understand which ticket to get for a specific ride.
The general rule is, that if you travel with regional means of transport (certain long-distance train categories and buses excluded) within the area of one transport authority, you pay according to the tariff set by this transport authority. If your trip starts and ends in areas covered by different transport authorities, you pay according to a tariff set by the specific transport operator. That can be DB (German Railways), but also a different private rail operator or a bus company. If different transport operators serve the same route, they may in this case have different ticket prices for the same route.
There is however an almost endless list of exceptions from these general rules. Neighbouring transport authorities often have special tariffs for crossing traffic, or there may be some overlaps in the geographical tariff coverage area. The area around Cottbus is served by VBB, one of the larger transport authorities in Germany. Just as an example: Their tariff and ticket conditions can be found in a 160 page publication.
Since Cottbus and Calau are both in the area served by VBB, your situation is relatively simple and covered by section B 5.5 in the conditions I linked to (continuation of a journey). It basically says, that if you already have a ticket for part of an intended journey, you need to buy an additional ticket valid from the last tariff zone you are travelling through and for which your existing ticket is valid to the new destination.
So in your case, if you want to go from A via B to C and you already have a valid ticket for A to B, you simply need to buy an additional ticket from B to C. It is not a requirement that the train actually stops in B for this to apply, but the train has to pass through B. If a direct train goes from A to C on a different route than via B, you will need a different ticket.
I am not quite sure why you are asking though. As you already write yourself: A ticket from anywhere in the area covered by your monthly ticket 'Cottbus AB' to Calau seem to cost the same, so it shouldn't matter if you buy the ticket for the entire trip or if you try to 'optimize' by using your monthly ticket for a part of it.
