The first home withdrawal is part of KiwiSaver and gives you the option to withdraw funds from your KiwiSaver account. It does not have the income and house price caps of the KiwiSaver HomeStart grant, but there are some eligibility criteria you will need to meet. Find out more about what you can withdraw and how to apply.
The KiwiSaver HomeStart grant is actually administered by, and run through, Housing New Zealand. The grant is a payment from them rather than from your KiwiSaver account. Find out more about the subsidy and whether you would be eligible.