Hi Puneet -
My apologies that nobody has responded to you on this yet ... I don't know that I have a clear, black-and-white answer for your question, as this is one of those areas where I think some of the lines definitely get a little blurry, but here's my interpretation of why things are the way they are in the PMBOK Guide ...
The Communications Management Plan is about how the messages are generated, sent, controlled, etc. In other words, this is the mechanical part of the communication. The stakeholder register tells us who needs to receive information and lets us know something about their needs and limitations when it comes to the communication media, but the focus here is on our communication protocols and making sure that we're setting proper expectations about how messages are to be sent and received, and what to do when exceptions occur (e.g. who to contact when key people are unavailable, etc.).
The Stakeholder Management Plan is about who needs to be engaged and how we need to go about increasing and/or maintaining their support. This has less to do with the mechanics and protocols and more to do with strategy and tactics. We need the stakeholder register to know who we're dealing with and what they expect, but rather than getting distracted by the nuts and bolts, we are focused on developing our strategy for keeping the right people happy and informed.
Whereas the Communications Management Plan how we are going to contact Mary Jenkins and how often she is to receive those communications, the Stakeholder Management Plan looks at the impact Mary Jenkins has on the project and what we need to do if we feel we might be losing her support at some point along the way.
It's easy to see how the Stakeholder Register feeds into both. At that point, the PMBOK Guide essentially has you answering two different questions at more or less the same time: how are we going to communicate with these people, and what can we do to keep those relationships on track? The questions are certainly related to some extent, and will be influenced by several of the same factors (including communications needs and preferences), but ultimately can be answered in either order and (mostly) independently of one another.
If you're still struggling to distinguish between the two, it might make more sense when you look at when and how each of these plans are used. In Monitor and Control Project Work, we generate the Work Performance Reports, which are inputs to Manage Communications. Here we are just needing to update our stakeholders on what's going on with day-to-day work, so we reference the Communications Management Plan for the "how." In contrast, if you look ahead to Manage Stakeholder Engagement, you'll see that both the Communications Management Plan and Stakeholder Management Plan are inputs. This makes sense - when issues arise and we need to engage our stakeholders, or when we need to seek additional input and feedback, we need to consider both the "how" and the "why," hence the reference to both plans.
I hope all of that made some sense - this is one of those things that is easier for me to understand than to actually articulate, so if anyone else has a better way to phrase this please feel free to jump in.