Sayak,
I would say that your experience falls under MM. To look at the structure, go to SAP's Help website: help.sap.com. Pick SAP Business Suite from the Help Portal section at the top. From the links on the side, pick SAP ERP. From the expanded links, pick SAP ERP 6.0. From the Application Help section, pick your preferred language (I'll assume English) for SAP ERP Central Component. From the links at the side under SAP ERP, pick SAP ERP Central Component. From the links on the left side, open up Logistics. From the areas under Logistics, I think that you'll find your experience fits in Materials Management (MM) and Logistics Execution (LE).
MM includes Inventory Management and Physical Inventory (and other things). LE includes Warehouse Management, Shipping, and Transportation (and other things). The only part of your skill set that's in SD would be Order Processing (and you can check out SD in Help as well, also under Logistics).
As for which has more jobs, I have no idea. I'd suggest logging on your favorite job board and comparing the results when you search for SAP + Sales and Distribution, and SAP + Materials Management.
In my opinion, the best way to learn is to get a job with a consulting firm based on your industry experience, and have them train you. Getting training on your own is no substitute for being able to develop your skills on a team.
Good luck,
- Jeff