System Analysis and Requirement Elicitation are to different things.
Requirement Elicitation also known as Requirement Analysis or Information Gathering is the practice undertaken by a system analysis in collecting information from users to him, the system analyst upgrade a system or build are new system to help the users of the system. The System Analyst could use the Interactive Method which is using questionnaires or interviewing users or the Unobtrusive Method which sampling and observing the users.
On the other hand System Analysis about what a system should do. This where the System Analyst monitors or analysis the system itself and identify the problem of the system and determine or develop a way of solving the problem of the system to benefit its users. The System Analyst may use the System Development Life Cycle (SDLC), the Agile Methodology or the Object-Oriented Methodology.