Essentially, yes. Safe Work Method Statements (SWMS) is the term used specifically for legally required documentation accompanying high risk construction work (HRCW), with formal specifications. However, it encompasses generic Job Hazard Analysis (JHA) or Job Safety Analysis (JSA).
In other words, a SWMS can fulfil the function of a JHA, but a basic JHA may not be a sufficient substitute for a SWMS, particularly for HRCW. This is why myosh offers a SWMS workflow to cover the most stringent of requirements.