Short answer: HomeStart is the old name for the First Home Grant. Same program, new name.
HomeStart was the old name for what is now called the First Home Grant. The rules are basically the same but the name changed. If someone mentions HomeStart, they mean the First Home Grant. Do not get confused by the old name.
Old Name: HomeStart Grant
New Name: First Home Grant
Amount: $5,000-$10,000
Change Date: 2019