The Single Expert Witness interviews the parties, observes interactions between children and parents et al and writes a report making recommendations to the Court.
The Independent Children's Lawyers role is a bit more involved given that they remain throughout the duration of the case (from the time of their appointment to discharge, the latter usually being at the finalisation of the orders/case).
ICL's take on a partially 'administrative' role (although some will meet the child/ren). Some of the roles they are meant to undertake (not all are created equal, as like all occupations/professions) are to assist the court by ensuring all substantive matters are before the court, try to assist parties to reach agreements, ensure parents (parties) remain focused in their decisions on the best interests of the child/ren, offer an impartial view of the case, ensure additional information is before the court (where needed) to name a few.
They are a third party to the case, so will also make submissions et al
Like the SEW, the ICL does not decide the matter, the Judge does, but both can bring more clarity of the issues in dispute and also assist the Court with additional, impartial, views/information.