While the differences between the business analyst (BA) and systems analyst (SA) vary from organization to organization, there are some acceptable differences:

Role and Responsibilities 

BA: The business analyst's main role is to understand the business processes and procedures (how the business works), to identify areas of improvement (problem areas), and to work with the business stakeholders to identify suitable solutions. If the solution involves the development or modification of information systems, the business analyst is also responsible to gather, analyze, and document the business requirements which must be fulfilled by the software.

SA: The systems analyst's main role is to understand the business requirements (documented by the business analyst) and to design and document the functional and, often, technical implementation of the software/IT system. The systems analyst also helps solve problems and issues with existing systems through research of these systems, code reviews, data analysis, etc.

Skills and Competencies

BA: Great communication and negotiation skills, vertical business/domain knowledge, ability to map and document business processes, requirements elicitation and documentation.

SA: Strong technical skills, excellent troubleshooting and debugging abilities, solid technical writing skills, system modeling/documentation skills (class diagrams, sequence diagrams, etc.), data analysis and modeling skills.

Summary

BA: Talks the business talk; understands the business.

SA: Talks the IT talk; understands the technology.

The reality is that the business analyst and systems analyst roles often overlap.  Many analysts who perform both roles have the title of "Business Systems Analyst."