The first is for those with school age children (5 to 18 years) and the second for people with pre-existing medical conditions. The grants are designed to help those eligible to get back on their feet financially. The grants are in the form of electricity heating subsidies.
More information, eligibility criteria, and application forms are available from these web pages:
Winter Assistance Grant for school aged children -hereWinter Assistance Grant for pre-existing medical conditions -hereA Winter Assistance for Under 5s Grant is already in existence and information is here, and a list of the whole range of NZ Red Cross grants is available here.