What is the difference between Business Analysis and System Analysis?

The line between business analyst role and systems analyst role is not a clear one .
As a profession, we might choose to distinguish the roles; giving the business analyst domain over the business and functional requirements and the systems analyst domain over the details of the system implementation.

Business Alaysis output is functional design.
In functional design use cases related to business processes are drawn then these use cases are further elaborated to contain business logic that encompasses inherent system and external system behaviour.
Further lastly the functional design document contains test cases and their result sets so that when the product is tested the testing team must test the product in line with functional design.
Now System Analysis is only limited to inherent system and has nothing to do with external systems.
Moreover it is limited to the behaviour of technical objects very unlike business analysis which is concerned with functional objects.
Further System Analysis can only be done once Functional Design has been approved, Therefore it would be safe to assume that Business Analysis is Functional understanding and System Analysis is technical understanding.

A Business Analyst needs to know the System because the last makes part of the first.
For instace if we need to make a business analysis it's fundamental the use of an information and the know how of any other system that makes part or is accessory of the referred business.

as Wikipedia - Systems analysis is the study of sets of interacting entities, including computer systems analysis.
This field is closely related to requirements analysis or operations research.
It is also "an explicit formal inquiry carried out to help someone (referred to as the decision maker) identify a better course of action and make a better decision than he might otherwise have made - Business analysis is a research discipline of identifying business needs and determining solutions to business problems.
Solutions often include a systems development component, but may also consist of process improvement, organizational change or strategic planning and policy development so Business analysis is type of systems analysis

the line between these two titles is too thin, and many times the terms have been used interchangeably.
it's very common to see companies hiring SA to do BA work or vice versa, moreover, some companies will use the term Business system analyst.
Business analysis is the process of identifying business needs and determining solutions to business problems.
these solution could be IT solutions or pure business operation and performance solutions.
for example, a company could hire a business analyst to dig down their marketing problem.
System analyst position, on the other hand, would be more inclined toward technical details, and usually, if not always, is related to the IT sector.

Systems analysts utilize an organization’s IT systems to help achieve strategic business goals. They may design and develop new systems by configuring new hardware and software, or use existing systems in new ways to accomplish additional or different outcomes.

Business analysts generally possess technical knowledge as well. Their main focus is identifying opportunities for improving a business’s processes and using technology to eliminate problems that affect productivity, output, distribution and ultimately, the bottom line. So, knowing how technology can solve business problems is vital to a business analyst’s success. These professionals require a high degree of specialized skills in order to solve business problems through a variety of typical job duties.