In SAP field, people are considered as consultants or managers.
Consultants do things and they are classified as technical or functional. (Please note some people consider consultants as those who work on the basis of an employment contract. I am referring to grouping based on what people do.)
People who manage tasks and people are Managers. A manager can be in any field – not necessarily in SAP. However a recruiter needs to know in which area a manager or consultant has worked.
As you have rightly said, you may take up something akin to your current background. I believe this would be the technical areas of: (a)Basis with emphasis on ESS/Internet server and similar functions, (b)Netweaver. Then you could grow to other areas – BW(Business Warehouse), CRM(Customer Relationship Management), SRM (Supplier Relationship Mgt), PLM (Product Lifecycle Mgt), and so on.
Programming is a technical area if you are interested. Here mainly ABAP is used. Knowledge in C++ and object oriented techniques help a lot.
Functional areas are Fi/CO, HCM, PP, MM, WM, SCM. If you are interested in these areas, you need to acquire the business skills. You can get the business knowledge by working with an implementation team or in a business area.
You may start with one speciality. Then after a period of say 1 or 2 years, you may expand or add other skills. From Technical area you may expand to Functional.
I am sure you’d know that anything would not come easily. You need to persevere and not give up.
Hope this helps. All the Best!