Consular support and assistance is largely practical in nature (e.g. having a representative present for a court appearance). An explanation of consular assistance can be found at https://smartraveller.gov.au/services/Pages/consular-services-charter.asp
Diplomatic support/intervention relates to intervention that may occur in a peaceful way that is sensitive to both parties. For example a minister from one country making representations about issues pertaining to the health and welfare of a national detained abroad to their counterpart from another country on humanitarian grounds e.g. recent support by Marise Payne for Kylie Moore-Gilbert
In October 2019 Julian’s lawyers asked for the Australian government’s assistance in dealing with their client’s inhumane conditions in Belmarsh prison which has led to, and is continuing to cause, serious damage to Julian’s health ref Sydney Morning Herald
Consular assistance is up and running – embassy officials are now attended hearings
The Julian’s Australian Legal Team is working with the Foreign Minister’s office.